Professor A.J. de Jong, Columbia university, Department of Mathematics.

At MIT I started having a graduate student algebraic gometry seminar. I have decided to put up this page to archive the topics of previous seminars. However, I have only gone as far back as the first seminar I organized here at Columbia.

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PAST SEMINARS-----------------------------------------

In the summer of 2020 the seminar was about derived categories of varieties leading up to the result that given a smooth proper variety over an algebraically closed field there are only a countable number of varieties derived equivalent to the given one. Here is the link to the webpage with information.

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In the Spring of 2020 the seminar was a "talk till you're stuck" experiment. It was cut short by the Covid-19 pandemic of 2020. Here is a link to the webpage with information.

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In the Fall of 2019 the seminar was on de Rham cohomology in characteristic zero as a Weil cohomology theory. Please see the webpage with information.

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In the Spring of 2019 the seminar was on Higgs bundles in positive characteristic. Please see the webpage with information.

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In the Fall of 2018 the seminar was on Topologies and Descent. Please see the webpage with information.

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In the Spring of 2018 the seminar was on local cohomology in algebraic geometry (following SGA2 and the exposition in the Stacks project). Please see the webpage with information.

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In the Fall of 2017 the seminar was a seminar on examples in algebraic geometry. Please see the webpage with information.

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In the Spring of 2017 the topic of the seminar was on Yves Andre's proof of the direct summand conjecture. Please see the webpage with information.

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In the Fall of 2016 the topic of the seminar was the work of Bjorn Poonen. Please see the webpage with information.

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In the Spring of 2016 the topic of the seminar was the stable rationality and the diagonal as discussed by Voisin, Totaro, culminating in a discussion of the recent paper by Hassett, Pirutka, and Tschinkel. Please see the old webpage and the actual webpage with information.

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In the Fall of 2015 the topic of the seminar was the Tate conjecture for surfaces over finite fields as discussed in Milne's paper "On a conjecture of Artin and Tate". Please see the webpage here.

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In the Spring of 2015 the topic of the smeinar was intersection theory and motives. Here is the link to the webpage.

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In the Fall of 2014 the topic of the seminar was tropical geometry and in particular the proof of the Brill-Noether theorem using tropical geometry. It was a really fun topic to do! Here is the link to the webpage.

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In the Spring of 2014 I organized a literature seminar for graduate students. Here is the link to the webpage.

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In the Fall of 2013 I organized a graduate student seminar on derived categories. Take a look at the webpage.

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In the Spring of 2012 I organized a graduate student seminar on crystalline cohomology. Take a look at the webpage. See graduate student seminar in algebraic geometry for the original course listing.

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During the Fall of 2011 I organized a graduate student seminar on Brauer groups in Algebraic Geometry. Take a look at its webpage for more information. See graduate student seminar in algebraic geometry for the original course listing.

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During the Spring of 2011 I organized a graduate student seminar on Derived Categories in Algebraic Geometry. Take a look at its webpage for more information. See graduate student seminar in algebraic geometry for the original course listing.

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During the Fall of 2010 I organized a graduate student seminar on Hodge Theory in Algebraic Geometry. Please find the original web-page with list of talks on this page. See graduate student algebraic geometry seminar for the original course listing.

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During the Summer of 2010 I organized a graduate student seminar on Algebraic Geometry. The idea was for the students and I to come up with problems in algebraic geometry, to democratically choose a problem, and try to solve that problem. If stuck or solved we start over. The rules will be that the problems

- are loosely speaking in the field of arithmetic algebraic geometry
- are easier than PhD problems and harder than most problems in Hartshorne,
- are not sub problems of a thesis problem anybody is working on.

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During the Spring of 2010 semester the graduate student algebraic geometry seminar was a literature seminar. Please look at this page for a list of papers. We met on Fridays from 3:30-4:30 (+/- 15 minutes) in Room 312 of the Mathematics Building. The first organizational meeting was a short meeting on Friday, January 22, 2010 where we divided up the talks. List of talks with names and topics is here.

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During the Fall of 2009 the
graduate student algebraic geometry seminar was on **algebraic stacks**.
We met Fridays from 10:30-12:30 in Room 312 of the Mathematics Building.
I gave the first two lectures to introduce the material, the first one on
Friday, September 11, 2009.
After the first two lectures the graduate students gave lecture on examples
of algebraic stacks,
especially those which are relevant to moduli theory,
and more generally arithmetic algebraic geometry.
Here is the (preliminary) list of topics for lectures by students:
pdf |
dvi |
tex.
List of talks (see file above for more details):

- Sept 25. Quotient stacks. Alice Rizzardo.
- Oct 2. Stacky Curves. Xue Hang.
- Oct 9. Finite coverings of DM stacks. Jarod Alper.
- Oct 16. Vector bundles on stacks. Qi You.
- Oct 23. Picard Stacks. Yanhong Yang.
- Oct 30. Coarse Moduli Spaces. Yi Zhu.
- Nov 6. GIT STacks. Alon Levy.
- Nov 13. No Seminar.
- Nov 20. Cohomology of stacks. Thibaut Pugin.
- Nov 27. No Seminar.
- Dec 4. Intersection theory stacks. Zachary Maddock.
- Dec 11. Algebraic Spaces.

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In the summer of 2009 we had a graduate student algebraic geometry seminar on Intersection Theory, organized by Qi You and myself. We worked through classical intersection theory including Grothendieck-Riemann-Roch.-----------------------------------------

In the Spring of 2009 the graduate student algebraic geometry seminar
was organized by Maksym Fedorchuk and me. The topic was be
*Introduction to higher dimensional algebraic geometry*.
Here is some more information:

- Please email me to get on the mailing list.
- Lectures will be Fridays 10:45 - 12:30 in Math 312.
- First organizational meeting: Friday January 23.
- First actual lecture: Friday January 30.
- List of talks: positivity.pdf
- Main reference: R. Lazarsfeld,
*Positivity in Algebraic Geometry*, Ergebnisse der Mathematik, 3 Folge, Volume**48**. - Other reference: R. Hartshorne,
*Ample subvarieties of algebraic varieties*, Lecture Notes in Mathematics**156**.

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In the Fall of 2008 the graduate student algebraic geometry seminar is organized by Frans Oort and me. The topic was ``Abelian Varieties over Finite Fields''. Main Literature Sources, with links:

- J. Tate,
*Classes d'isog\'enies de vari\'et\'es ab\'eliennes sur un corps fini (d'\`apres T. Honda)*, S\'em. Bourbaki**21**(1968/69), Exp. 352. Link. - F. Oort,
*Abelian varieties over finite fields*, In: Higher-dimensional geometry over finite fields, Advanced Study Institute 2007 Proceedings (Editors: Y. Tschinkel and D. Kaledin). Link1 and Link2. -
J. Tate,
*Endomorphisms of abelian varieties over finite fields*, Invent. Math.**2**(1966), 134-144. Link. - Very detailed exposition of Complex Multiplication written up as notes for the 2005-05 VIGRE number theory working group. Organized by Brian Conrad and Chris Skinner. Link

- Homepage of Frans Oort at Columbia University Link.
- Homepage of Frans Oort at Utrecht University Link.
- List of talks and overview of the seminar: pdf-file or dvi-file .
- Here (pdf-file and dvi-file) is a short note describing how to find all q-Weil numbers of degree exactly 4 over Q. Here is a pari script to list all minimal polynomials of q-Weil numbers of degree 4 over Q, based on the note above. And finally here are the lists for q = 2, 3, 4.

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In the fall of 2008 the graduate student algebraic geometry seminar was about weighted projective spaces, quasi-smooth hypersurfaces in them, and how to compute their cohomology. Ostensibly the title was "Problems for graduate students". I gave all of the lectures myself.

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In the Summer of 2008 we had a graduate student seminar on A^1-homotopy theory where all the lecture were given by Bhargav Bhatt.

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The Fall semester of 2007 we discussed motives in the graduate student algebraic geometry seminar. Here are some related documents:

- and a list of literature is here.
- A short discussion of intersection theory (as used in the seminar) is here.
- A short discussion of Weil cohomology theories (as used in the seminar) is here.
- A short discussion of algebraic de Rham cohomology as a Weil cohomology theory is here.

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In the summer of 2007 the graduate student algebraic geometry seminar was about GIT and Hodge theory.

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In the Spring of 2007 the topic of the graduate student algebraic geometry seminar was "Rational curves on higher dimensional algebraic varieties -- in particular low degree hypersurfaces". Jason Starr and I alternated giving the lectures, and we worked through the paper "Low degree complete intersections are rationally simply connected" available on Jason Starr's webpage.

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Fall 2006: Topic was deformation theory.

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Spring 2006: Topic was algebraic stacks.