David Hansen

I'm a Ritt assistant professor here at Columbia. I like algebra and number theory, especially *p*-adic Hodge theory and *p*-adic aspects of the Langlands program. Previously I was a postdoc at l'Institut de Mathematiques de Jussieu. During 2010-2013 I was a Ph.D. student at Boston College, where my advisor was Avner Ash. I graduated from Brown University in May 2010 with a B.A. in mathematics. Here's my CV.

This semester I'm teaching Honors Math A and Number Theory and Cryptography.

**My Address:**

Room 516

Department of Mathematics

Columbia University

2990 Broadway

New York, NY 10027

lastname @ math.columbia.edu

Want me to referee something? Read this first.

Papers and Preprints

**Remarks on nearby cycles of formal schemes** (* **pdf *)

Preprint (version of 5/9/2018)

**Vanishing and comparison theorems in rigid analytic geometry** (* **pdf *)

Preprint (version of 3/14/2018)

**A primer on reflexive sheaves**, an appendix to** On the Kottwitz conjecture for local Shimura varieties** (* **pdf | **arxiv *) by T. Kaletha and J. Weinstein

Preprint (version of 9/19/2017)

**On p-adic L-functions for Hilbert modular forms** (

Preprint (version of 10/15/2017)

**Line bundles on rigid varieties and Hodge symmetry** ( *pdf *| *arxiv *), with S. Li

Preprint (version of 8/3/2017)

**Degenerating vector bundles in p-adic Hodge theory** (

Preprint (version of 7/3/2017)

**Extensions of vector bundles on the Fargues-Fontaine curve** ( *pdf *| *arxiv *), with C. Birkbeck, T. Feng, S. Hong, Q. Li, A. Wang and L. Ye

Preprint (version of 6/14/2017)

**Moduli of local shtukas and Harris's conjecture, I** ( *pdf *)

Preprint (version of 8/3/2016)

**Period morphisms and variations of p-adic Hodge structure** (

Preliminary draft (version of 5/6/2016). The next version will be rather seriously revised - in the meantime, here's an Oberwolfach report.

**Quotients of adic spaces by finite groups** (* pdf *)

*Math. Res. Letters*, to appear.

**On the GL _{n}-eigenvariety and a conjecture of Venkatesh** (

**Overconvergent modular forms and perfectoid Shimura curves** (* pdf *| *arxiv *|* journal *), with P. Chojecki and C. Johansson

*Documenta Math.*, Vol. 22, pp. 191-262.

**Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions** (

Preprint (version of 6/15/2016)

**Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality** (

**Minimal modularity lifting for GL _{2} over an arbitrary number field** (

**Shimura lifts of half-integral weight modular forms arising from theta functions** ( *pdf** *), with Y. Naqvi

*The Ramanujan Journal*, Vol. 17 No. 3 (2008)

Other writings

Warning: I haven't edited some of these very carefully. Also, some of these have been cannibalized by "official" papers above.

**Artin vanishing in rigid analytic geometry** (* **pdf *)

Obsolete shorter version of the paper "Vanishing and comparison..." above. Version of 8/24/2017

**Some remarks on Banach-Colmez spaces and related diamonds** (*pdf *)

The ideas sketched here are fully developed in the paper "Extensions..." above. Version of 3/3/2017.

** p-adic Hodge theory** (

Notes from a graduate topics class I taught at Columbia in Fall 2016. Unedited; use at your own risk!

**Smoothness of Bun _{n} for dinguses** (

A letter to Jared Weinstein. Version of 12/25/2016.

**Notes on shtukas and Harris's conjecture** (*pdf *)

A letter to Jared Weinstein. Version of 5/24/2016.

**Period maps, variations of p-adic Hodge structure, and Newton stratifications** (

An announcement (?) of some results in the paper "Period morphisms..." above.

**Notes on diamonds** (*pdf *)

Version of 8/25/2016. Warning: These are outdated, since the definition of diamonds changed subsequent to this writing.

**Motivic cohomology actions and the geometry of eigenvarieties** (*pdf *)

Notes on my paper with Jack.

**A canonical two-variable p-adic L-function over the eigencurve** (

Some version of this material will appear in "Iwasawa theory of overconvergent modular forms, II".

** p-adic geometry, d'apres Peter Scholze** (

Notes from an informal lecture series I gave at Columbia in Spring 2015, on Scholze's Berkeley course and related material. Most everything of interest here is redone more carefully and correctly in the "Notes on diamonds" above.

**Overconvergent cohomology: theory and applications** (*pdf *)

My PhD thesis; everything here has been incorporated into "Universal eigenvarieties..."

**The Petersson norm of the Jacobi theta function** (*pdf *)

**What is a spectral sequence?** (*pdf* )

**Pairings on modules of analytic distributions** (*pdf *)

**The Gross-Zagier formula: a brief introduction** (*pdf* )

Notes for a talk in the Harvard graduate student number theory seminar, March 2011.

**Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields** (*arxiv* |* pdf *)

This is an extract from my Brown senior thesis.

**The arithmetic of elliptic curves** (*pdf* )

Notes for a talk I gave to some undergraduates at Williams College, November 2008.