Expository articles and presentations

Here are links to expository articles I have written. There is large variation in their quality and length, they are aimed toward a wide variety of audiences, and they have generally not been proofread, so use at your own risk!

Algebraic geometry

  • Cohen-Macaulay rings
  • Riemann surfaces are algebraic
  • Standard conjectures
  • Six functor formalisms
  • Derived infinity categories

    • Arithmetic geometry and number theory

  • Artin-Verdier duality
  • Complex multiplication of eliiptic curves
  • Mordell-Weil
  • Reciprocity laws
  • The Tate conjecture
  • Weil conjectures for abelian varieties
  • Weil conjectures for curves

    • Topology

  • Atiyah-Hirzebruch
  • Bott periodicity
  • cohomological descent
  • Dold-Kan
  • J-homomorphism

    • Differential equations

  • Riemann-Hilbert
  • Gauss-Manin

    • And here are some slides for presentations.

  • anabelian geometry
  • motivic cohomology
  • Grothendieck