Publications

Articles (Warning: links may be to uncorrected preliminary drafts.)

• [1]

  Harris, M.: Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields.
  Inventiones Math. 51, 123-141 (1979).

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• [2]

  Harris, M.: A note on three lemmas of Shimura.
  Duke Math. J., 46, 871-879 (1979).

• [3]

  Harris, M.: P-adic representations arising from descent on abelian varieties. Compositio Math. 39, 177-245 (1979); Correction, Compositio Math. (2000).

  [See ERRATA page at http://www.math.columbia.edu/~harris/website/errata-publications-list-links-here for comments]

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• [4]

  Harris, M.: Kubert-Lang units and elliptic curves without complex multiplication. Compositio Math. 41, 127-136 (1980).

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• [5]

  Harris, M.: The rationality of holomorphic Eisenstein series. Inventiones Math. 63, 305-31 (1981).

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• [6]

  Harris, M.: Special values of zeta functions attached to Siegel modular forms. Annales Scient. de l'Ec. Norm. Sup., 14, 77-120 (1981).

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• [7]

  Harris, M.: Maass operators and Eisenstein series. Math. Ann. , 258, 135-144 (1981).

• [8]

  Harris, M.: P-adic measures for spherical representations of reductive p-adic groups. Duke Math. J. 49, 497-512 (1982).

• [9]

  Harris, M., Jakobsen, H.P.: Singular holomorphic representations and singular modular forms. Math. Ann., 259, 227-244 (1982).

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• [10]

  Harris, M., Jakobsen, H.P.: Covariant differential operators, in Group Theoretical Methods in Physics (Istanbul, 1982), Lecture Notes in Physics, 180, 16-34. Berlin: Springer-Verlag (1983).

• [11]

  Harris, M.: Eisenstein series on Shimura varieties. Ann. of Math., 119, 59-94 (1984)

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• [12]

  Harris, M.: Arithmetic vector bundles on Shimura varieties, in Automorphic Forms of Several Variables, Proceedings of the Taniguchi Symposium, Katata, 1983 , 138-159. Birkhaüser (1984).

• [13]

  Harris, M.: Arithmetic vector bundles and automorphic forms on Shimura varieties. I. Inventiones Math., 82, 151-189 (1985).

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• [14]

  Harris, M.: Arithmetic vector bundles and automorphic forms on Shimura varieties II. Compositio Math., 60, 323-378 (1986).

• [15]

  Harris, M., Phong, D. H.: Cohomologie de Dolbeault à croissance logarithmique à l'infini. C. R. Acad. Sci. Paris, 302, 307-310 (1986).

• [16]

  Harris, M.: Formes automorphes "géométriques" non-holomorphes: Problèmes d'arithméticité, in Sém de Théorie des Nombres, Paris 1984-85 Boston: Birkhaüser (1986).

• [17]

  Harris, M.: Arithmetic of the oscillator representation, manuscript (1987), revised (2005).

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• [18]

  Harris, M.: Functorial properties of toroidal compactifications of locally symmetric varieties, Proc. Lon. Math. Soc., 59, 1-22 (1989)

• [19]

  Harris, M.: Automorphic forms and the cohomology of vector bundles on Shimura varieties, in L. Clozel and J.S. Milne, eds., Proceedings of the Conference on Automorphic Forms, Shimura Varieties, and L-functions, Ann Arbor, 1988, Perspectives in Mathematics, New York: Academic Press, Vol. II, 41-91 (1989).

• [20]

  Harris, M.: Automorphic forms of d-bar -cohomology type as coherent cohomology classes, J. Diff. Geom., 32, 1-63 (1990).

• [21]

  Harris, M.: Period invariants of Hilbert modular forms, I: Trilinear differential operators and L-functions, in J.-P. Labesse and J. Schwermer, eds., Cohomology of Arithmetic Groups and Automorphic Forms, Luminy, 1989, Lecture Notes in Math., 1447, 155-202 (1990).

• [22]

  Harris, M., Kudla, S.: The central critical value of a triple product L-function, Ann. of Math., 133, 605-672 (1991).

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• [23]

  Harris, M., Kudla, S.: Arithmetic automorphic forms for the non-holomorphic discrete series of GSp(2), Duke Math. J., 66, 59-121 (1992).

• [24]

  Garrett, P.B., Harris, M.: Special values of triple product L-functions, Am. J. Math., 115, 159-238 (1993).

• [25]

  Harris, M.: Non-vanishing of L-functions of 2x2 unitary groups, Forum Math., 5, 405-419 (1993).

• [26]

  Harris, M., Soudry, D., Taylor, R.: l-adic representations attached to modular forms over an imaginary quadratic field, I: lifting to GSp(4,Q), Inventiones Math., 112, 377-411 (1993).

• [27]

  Harris, M.: L-functions of 2 by 2 unitary groups and factorization of periods of Hilbert modular forms, J. Am. Math. Soc., 6, 637-719, (1993).

• [28]

  Harris, M., Zucker, S.: Boundary cohomology of Shimura varieties, I: coherent cohomology on the toroidal boundary, Annales Scient. de l'Ec. Norm. Sup., 27, 249-344 (1994).

• [29]

  Harris, M., Zucker, S.: Boundary cohomology of Shimura varieties, II: mixed Hodge structures , Inventiones Math., 116, 243-307 (1994); Erratum, Inventiones Math., 123, 437 (1995).

• [30]

  Harris, M.: Hodge-de Rham structures and periods of automorphic forms, in Motives, Proc. Symp. Pure Math. AMS, 55, Part 2, pp. 573-624 (1994).

• [31]

  Blasius, D., Harris, M., Ramakrishnan, D.: Coherent cohomology, limits of discrete series, and Galois conjugation, Duke Math. J., 73, 647-686 (1994).

• [32]

  Harris, M.: Period invariants of Hilbert modular forms, II, Compositio Math., 94, 201-226 (1994).

• [33]

  Harris, M., Kudla, S., Sweet, W. J.: Theta dichotomy for unitary groups, J. Am. Math. Soc., 9, 941-1004 (1996).

• [34]

  Harris, M.: Supercuspidal representations in the cohomology of Drinfel'd upper half spaces; elaboration of Carayol's program, Inventiones Math., 129, 75-119 (1997).

• [35]

  Harris, M.: L-functions and periods of polarized regular motives, J.Reine Angew. Math., 483, 75-161 (1997).

• [36]

  Harris, M. , Li, J.-S.: A Lefschetz property for subvarieties of Shimura varieties, J. Alg. Geom., 7, 77-122 (1998).

• [37]

  Harris, M.: The local Langlands conjecture for GL(n) of a p-adic field, n < p, Inventiones Math., 134, 177-210 (1998).

• [38]

  Harris, M.: Cohomological automorphic forms on unitary groups, I: rationality of the theta correspondence, Proc. Symp. Pure Math, 66.2, 103-200 (1999).

• [39]

  Harris, M.: Galois properties of cohomological automorphic forms on GL(n), J. Math. Kyoto Univ., 39, 299-318 (1999).

• [40]

  Harris, M., Tilouine, J.: p-adic measures and square roots of triple product L-functions, Math. Ann., 320, 127-147 (2001).

• [41]

  Harris, M., Scholl, A.: A note on trilinear forms for reducible representations and Beilinson's conjectures, J. European Math. Soc., 3, 93-104 (2001).

• [42]

  Harris, M., Zucker, S.: Boundary cohomology of Shimura varieties, III: Coherent cohomology on higher-rank boundary strata and applications to Hodge theory, Mémoires de la SMF, 85 (2001).

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• [43]

  Harris, M., Taylor, R.: The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, 151 (2001).

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• [44]

  Harris, M.: Local Langlands correspondences and vanishing cycles on Shimura varieties, Proceedings of the European Congress of Mathematics, Barcelona, 2000; Progress in Mathematics, 201, Basel: Birkhaüser Verlag, 407-427 (2001)

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• [45]

  Harris, M., Taylor, R.: Regular models of certain Shimura varieties, Asian J. Math., 6, 61-94 (2002).

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• [46]

  Harris, M.: On the local Langlands correspondence, in Proceedings of the International Congress of Mathematicians, Beijing 2002, Vol II, 583-597.

• [47]

  Harris, M., Taylor, R.: Deformations of automorphic Galois representations (manuscript, 1998-2003), see [56].

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• [48]

  Harris, M., Kudla, S.: On a conjecture of Jacquet, in H. Hida, D. Ramakrishnan, F. Shahidi, eds., Contibutions to automorphic forms, geometry, and number theory (collection in honor of J. Shalika), 355-371 (2004).

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• [49]

  Harris, M.: Occult period invariants and critical values of the degree four L-function of GSp(4), in H. Hida, D. Ramakrishnan, F. Shahidi, eds., Contibutions to automorphic forms, geometry, and number theory (collection in honor of J. Shalika), 331-354 (2004).

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• [50]

  Harris, M., Labesse, J-P.: Conditional base change for unitary groups, Asian J. Math., 8 (2004) 653-684.

• [51]

  Harris, M.: The Local Langlands correspondence: Notes of (half) a course at the IHP, Spring 2000, in J. Tilouine, H. Carayol, M. Harris, M.-F. Vignéras, eds., Formes Automorphes, Astérisque, 298 (2005) 17-145.

• [52]

  Harris, M., Li, J.-S., and Skinner, C.: The Rallis inner product formula and p-adic L-functions, in J. Cogdell et al., eds, Automorphic Representations, L-functions and Applications: Progress and Prospects, Berlin: de Gruyter, 225-255 (2005).

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• [53]

  Harris, M., Li, J.-S., Skinner, C.: p-adic L functions for unitary Shimura varieties, I : Construction of the Eisenstein measure, Documenta Math., Extra Volume: John H. Coates' Sixtieth Birthday 393-464 (2006).

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• [54]

  Harris, M. : A simple proof of rationality of Siegel-Weil Eisenstein series, in W.-T. Gan, S. Kudla, Y. Tschinkel, eds, Eisenstein Series and Applications, Boston: Birkhauser Perspectives in Mathematics, 258, 149-186 (2007).

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• [55]

  Harris, M.: Cohomological automorphic forms on unitary groups, II: period relations and values of L- functions, in Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory, Vol. 12, Lecture Notes Series, Institute of Mathematical Sciences, National University of Singapore (special issue in honor of R. Howe’s 60th birthday), 89-150 (2007).

• [56]

  Clozel, L., Harris, M., Taylor, R. : Automorphy for some l-adic lifts of automorphic mod l Galois representations, Publ. Math. IHES, 108, 1-181 (2008).

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• [57]

  Harris, M.: Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications, in Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin, Vol II, Boston: Birkhäuser, Progress in Mathematics, 270 (2009) 1-23

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• [58]

  Harris, M., Shepherd-Barron, N, Taylor, R.: A family of Calabi-Yau varieties and potential automorphy, Annals of Math., 171, 779-813 (2010).

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• [59]

  Harris, M.: Arithmetic applications of the Langlands program, Japanese J. Math., 3rd ser., 5 (2010) 1-71.

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• [60]

  Guralnick, R., Harris, M., Katz, N. : Automorphic realization of Galois representations, J. Euro. Math. Soc., 12, (2010) 915–937.

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• [61]

  Harris, M. : An introduction to the stable trace formula, in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. The stable trace formula, Shimura varieties, and arithmetic applications. Volume I: Stabilization of the trace formula, Boston: International Press (2011) 3-47.

• [62]

  Clozel, L., Harris, M., Labesse, J.-P.: Endoscopic transfer, in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. The stable trace formula, Shimura varieties, and arithmetic applications. Volume I: Stabilization of the trace formula, Boston: International Press (2011) 475-496.

• [63]

  Clozel, L., Harris, M., Labesse, J.-P.: Construction of automorphic Galois representations, I., in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. The stable trace formula, Shimura varieties, and arithmetic applications. Volume I: Stabilization of the trace formula, Boston: International Press (2011) 497-527.

• [64]

  Harris, M., Li, J.-S., Sun, Binyong, Theta correspondence for close unitary groups, Advanced Lectures in Mathematics, 19 (special issue in honor of S. Kudla) (2011) 265-308.

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• [65]

  Barnet-Lamb, T., Geraghty, D., Harris, M., and Taylor, R. : A family of Calabi-Yau varieties and potential automorphy II, Publications RIMS, 47 (2011) 29-98.

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• [66]

  Chenevier, G., Harris, M.: Construction of automorphic Galois representations, II, Cambridge J. Math., 1 (2013), 53-73.

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• [67]

  Harris, M.: The Taylor-Wiles method for coherent cohomology, J. Reine Angew. Math., 679 (2013) 125-153.

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• [68]

  Harris, M.: L-functions and periods of adjoint motives, Algebra and Number Theory, 7 (2013) 117-155.

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• [69]

  Harris, M.: Beilinson-Bernstein localization over Q and periods of automorphic forms, International Mathematics Research Notices, 2013 (2013) 2000-2053; Erratum, doi:10.1093/imrn/rny043

• [70]

  Harris, M.: Weight zero Eisenstein cohomology of Shimura varieties via Berkovich spaces, Pacific J. Math. (supplement to special issue in memory of J. Rogawski), 268 (2014), 275–281.

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• [71]

  Harris, M.: Testing rationality of coherent cohomology of Shimura varieties, in J. Cogdell et al., eds, Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, Contemporary Mathematics, 614 (2014) 81-95.

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• [72]

  Harris, M,: Galois representations, automorphic forms, and the Sato-Tate Conjecture, Indian Journal of Pure and Applied Mathematics, 45, (2014) 707-746.

• [73]

  Harris, M.: Automorphic Galois representations and the cohomology of Shimura varieties, in Proceedings of the International Congress of Mathematicians, Seoul 2014.

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• [74]

  Grobner, H., Harris, M.: Whittaker periods, motivic periods, and special values of tensor product L-functions, Journal of the Institut de Mathématiques de Jussieu, 15 (2016) 711-769.

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• [75]

  Grobner, H., Harris, M., Lapid, E.: Whittaker regulators and non-critical values of Asai L-functions, Contemporary Mathematics, 664 (2016) 119-134.

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• [76]

  Harris, M., Lan, K-W., Taylor, R., and Thorne, J., On the rigid cohomology of certain Shimura varieties, Research in the Mathematical Sciences, Special Collection in honor of Robert Coleman, 3: 39, (2016)

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• [77]

  Harris, M.: p-adic and analytic properties of period integrals and values of L-functions, Annales des Mathématiques du Québec, 40(2) (2016) 435-452, special issue in honor of G. Stevens.

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• [78]

  Harris, M.: Speculations on the mod p representation theory of p-adic groups, Annales de la Faculté des sciences de Toulouse, 25, (2016) 403-418, special issue in honor of V. Schechtman.

• [79]

  Harris, M., Lin, J.: Period relations and special values of Rankin-Selberg L-functions, in J. Cogdell, J.-L. Kim, C.-B. Zhu, eds., Representation Theory, Number Theory, and Invariant Theory, In Honor of Roger Howe on the Occasion of His 70th Birthday, Progress in Math. 323 (2017).

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• [80]

  Esnault, H., Harris, M.: Chern classes of automorphic vector bundles, Pure and Applied Mathematics Quarterly, 13 (2017) 193–213.

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• [81]

  Harris, M., Venkatesh, A.: Derived Hecke algebra for weight one forms, Experimental Mathematics, 28 (2019) 342–361.

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• [82]

  Böckle, G., Harris, M., Khare, C., Thorne, J.: G^􏰊-local systems on smooth projective curves are potentially automorphic, Acta Mathematica, 223:1 (2019) 1-111.

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• [83]

  Esnault, H., Harris, M.: Chern classes of automorphic vector bundles, II Epijournal de géométrie algébrique, 3 (2019), article no. 14.

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• [84]

  Calegari, F., Geraghty, D., Harris, M.: Bloch-Kato conjectures for automorphic motives, Appendix to Calegari, F., Geraghty, D., Minimal modularity lifting for non-regular symplectic representations, Duke Math. J., 169 (2020) 801-896.

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• [85]

  Eischen, E., Harris, M., Li, J.-S., Skinner, C.: p-adic L functions for unitary Shimura varieties, II : zeta integral calculations; III : ordinary families and p-adic L-functions, Forum of Mathematics, Pi (2020) Vol. 8, e9, doi:10.1017/fmp.2020.4

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• [86]

  Harris, M. Curvas de Shimura, notes of a course given in Cusco, Perú in 2015, in Mikhail Belolipetsky,
  Harald Andrés Helfgott, Carlos Gustavo Moreira, eds., Aritmética, grupos y análisis - Actas de la escuela AGRA II, Publicações Matemáticas No 42 Instituto de Matemática Pura e Aplicada (2020).

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• [87]

  Harris, M., Shimura varieties for unitary groups and the doubling method, in Relative Trace Formulas (Proceedings of the Simons Symposium) (2021) 217-252.

• [88]

  Harris, M., Khare, C., Thorne, J., A local Langlands parameterization for generic supercuspidal representations of $p$-adic $G_2$, Ann. Sci. ENS, 56 257--286.

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• [89]

  Harris, M.: Incorrigible representations

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• [90]

  Harris, M. Square root $p$-adic $L$-functions, I: Construction of a one-variable measure, Tunisian J. Math., 3, (2021) 657-688.

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• [91]

  Darmon, H., Harris, M., Rotger, V., Venkatesh, A.: Motivic cohomology and the derived Hecke algebra for dihedral weight one forms. Michigan Math. J., 72 (2022), 145–207, special issue in honor of Gopal Prasad.

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• [92]

  Feng, T., Harris, M., Mazur, B.: Derived class field theory, ICCM Notices, 11 (2023) 88-98.

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• [93]

  Böckle, G., Feng, T., Harris, M., Khare, C., Thorne, J.: Cyclic base change of cuspidal automorphic representations over function fields, Compositio Math (in press).

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• [94]

  Gan, W.-T., Harris, M., Sawin, W.: Local parameters of supercuspidal representations, with Appendix by R. Beuzart-Plessis, Forum of Math, Pi , 12 (2024) e13.

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• [95]

  Harris, M.: Local Langlands correspondences, article to appear in the proceedings of the conference in honor of Steve Kudla's 70th birthday.

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• [96]

  Feng, T., Harris, M.: Derived aspects of the Langlands correspondence, notes for IHES 2022 summer school (manuscript, May 2022).

• [97]

  Ciubotaru, D., Harris, M.: On the generalized Ramanujan and Arthur conjectures over function fields, https://arxiv.org/abs/2311.15300 [math.NT]

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• [98]

  Atanasov, S, Harris, M.: The Taylor-Wiles method for coherent cohomology, II, arXiv:2112.06851 [math.NT].

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• [99]

  Grobner, H., Harris, M., Lin, J.: Deligne's conjecture for automorphic motives over CM-fields

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