Jesse

Writing

Research

Notes

  • Degenerating the Jacobian: This is a poster I presented at the conference The View from Joe's Office (Aug 278, 2011).
  • Local Structure of Compactified Jacobians: These are slides from a talk I gave at the 2011 Joint Meetings. (Jan 7, 2011. Updated April 15, 2011)
  • The Chow Ring of a Blow-up: This is a short note explaining how to compute the Chow Ring of the blow-up of projective 3-space along the rational normal curve. This computation was suggested as an interesting short project in William Fulton's course on intersection theory. (Winter 2010)
  • A Non-Reduced Picard Scheme: I was shocked to hear that the Picard scheme of a smooth projective surface in positive characteristic can be non-reduced. Igusa's paper on this topic was written in the language of Weil's Foundations and his language is somewhat difficult for a modern student of algebraic geometry to understand. This paper is the product of my attempt to translate Igusa's arguments into the language of modern scheme theory. When I "have some free time", I hope to give equations for Igusa's surface. (Winter 2007, Revised March 2008)
  • Notes on Néron Models: These are notes on Néron models for a talk that I gave in a student seminar. At a later date, I hope to add Raynaud's example illustrating the failure of the comparision theorem when the residue field is not assumed to be perfect. (Fall 2007)
  • Notes on Compactified Jacobians: These are notes on compactified Jacobians for a talk that I gave. (Fall 2007)
  • Notes on Abelian Schemes: These are my notes on Abelian schemes based on a lecture of Brian Conrad's given at a seminar on finite groups schemes and p-divisible groups at Oberwolfach. The exercises assigned at the seminar can be found at the bottom of Brian's website. (Summer 2005)
  • Notes on Dieudonne modules: Here are my notes on Dieudonne modules based on another one of Brian's talks at the Oberwolfach seminar. (Summer 2005)

Reading Course

    In Fall of 2005, I organized a reading course on Geometric Class Field Theory under the supervision of Dennis Gaitsgory. We worked through both the classical proof and the more modern proof. The main references were Serre's book Algebraic Groups and Class Fields and Dennis Gaitsgory's brain. Below are some notes that were written as part of the reading course.

  • Abelian Covers and Generalized Jacobians: These are my notes on the classical approach to constructing abelian covers via generalized Jacobians. (In need of further editing)
  • Function-Sheaf Correspondence: These are Sug Woo Shin's notes on the Grothendieck function-sheaf correspondence.
  • Generalized Jacobians: These are my notes on constructing the generalized Jacobian of a curve. (In need of further editing)
  • Symmetric Powers: These are Sug Woo Shin's notes on symmetric powers. This material was needed for part of the modern proof of geometric CFT.