David Hansen

I'm an Associate Professor in the Department of Mathematics at the National University of Singapore. I'm broadly interested in arithmetic geometry and the Langlands program, and most of my work has a *p*-adic flavor.

**Spring 2024 categorical local Langlands seminar**

**my CV**

**my blog**

**Rampage seminar (2020-2022)** Here is an **archive of the video recordings**!

**My Address:**

Department of Mathematics

National University of Singapore

Level 4, Block S17

10 Lower Kent Ridge Road

Singapore 119076

dhansen%%%@%%%nus.edu.sg (remove %%%`s)

Papers and Preprints

**Beijing notes on the categorical local Langlands conjecture** (* pdf *)

Preprint. Videos available here.

**Arithmetic properties of l-adic etale cohomology and nearby cycles of rigid analytic spaces** (

Preprint (version of 12/29/2022)

** p-adic sheaves on classifying stacks, and the p-adic Jacquet-Langlands correspondence** (

Preprint (version of 6/28/2022)

**An enhanced six-functor formalism for diamonds and v-stacks** (* pdf *), with D. Gulotta and J. Weinstein

Preprint (version of 3/18/2022)

**Relative perversity** (* pdf *), with P. Scholze

*Communications of the AMS*, Vol. 3, pp. 631-668

**On the Kottwitz conjecture for local shtuka spaces** (* pdf *), with T. Kaletha and J. Weinstein

*Forum of Math. Pi,* Vol. 10 e13

**Weakly de Rham complexes** (* pdf *)

*TIFR Colloquium Proceedings*, to appear

**The six functors for Zariski-constructible sheaves in rigid geometry** (* pdf *), with B. Bhatt

*Compositio Math.*, Vol. 158 Issue 2, pp. 437-482

**On the supercuspidal cohomology of basic local Shimura varieties** (* pdf *)

*J. reine angew. Math.*, to appear

**Sheafiness criteria for Huber rings** ( *pdf* ), with K. Kedlaya

Preprint (version of 10/25/2022)

**Perfectoid Shimura varieties and the Calegari-Emerton conjectures** ( *pdf* ), with C. Johansson

*J. London Math. Soc.*, to appear

**Perfectoid quotients of the Lubin-Tate tower, revisited**, an appendix to **A quotient of the Lubin-Tate tower II** ( *pdf* ) by C. Johansson and J. Ludwig

*Math. Annalen*, Vol. 380, pp. 43-89.

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

Preprint (version of 5/9/2018)

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

*Compositio Math.*, Vol. 156 Issue 2, pp. 299-324.

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

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

*Math. Zeit.* Vol. 296, pp. 1777-1786

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

**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

*J. Inst. Math. Jussieu*, Vol. 21 Issue 2, pp. 487-532

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

*Tunisian J. Math.* Vol. 3 (4), pp. 749-799

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

Preliminary draft (version of 5/6/2016), never to be revised. Note that the Tannakian definition of

**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)

Slides

**Local Shimura varieties - past, present, future** ( *pdf *)

Lecture at the Rapoport 75th birthday conference. First 20 minutes on the board missing, replacement squid available here.

**Categorical local Langlands conjecture: refinements, questions, and speculations** ( *pdf *)

**Recent developments in etale cohomology** ( *pdf *)

**Local Shimura varieties and their cohomology** ( *pdf *)

**Sketch of the main geometric argument in HKW** ( *pdf *)

This was the fourth part of a six-part minicourse given jointly with Anschütz, Kaletha, Le Bras, and Weinstein.

Other writings

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

**Notes on relative perverse t-structures** (*pdf* )

Version of 4/27/2022.

**Notes on ULA complexes** (*pdf* )

Version of 1/9/2019.

**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 *)

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.