David Hansen

I'm a Research Group Leader / W2 professor at the Max Planck Institute for Mathematics in Bonn. I like algebra and number theory, especially p-adic Hodge theory and p-adic geometry, and p-adic aspects of the Langlands program.

my CV
my blog
Rampage seminar

My Address:
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn, Germany
dhansen%%%@%%%mpim-bonn.mpg.de (remove %%%`s)

Papers and Preprints

Relative perversity ( pdf ), with P. Scholze
Preprint (version of 9/13/2021)

On the Kottwitz conjecture for local shtuka spaces ( pdf ), with T. Kaletha and J. Weinstein
Preprint (version of 5/7/2021)

Weakly de Rham complexes ( pdf )
Preprint (version of 2/4/2021)

The six functors for Zariski-constructible sheaves in rigid geometry ( pdf ), with B. Bhatt
Compositio Math., to appear

On the supercuspidal cohomology of basic local Shimura varieties ( pdf )
Preprint (version of 5/6/2021)

Sheafiness criteria for Huber ringspdf ), with K. Kedlaya
Preprint (version of 9/7/2021)

Perfectoid Shimura varieties and the Calegari-Emerton conjecturespdf ), with C. Johansson
Preprint (version of 11/8/2020)

Perfectoid quotients of the Lubin-Tate tower, revisited, an appendix to A quotient of the Lubin-Tate tower IIpdf ) 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 ( pdf arxiv ), with J. Bergdall
Memoirs of the AMS, to appear

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 ( pdf )
J. Inst. Math. Jussieu, to appear.

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, to appear.

Moduli of local shtukas and Harris's conjecture ( pdf )
Tunisian J. Math., to appear.

Period morphisms and variations of p-adic Hodge structurepdf )
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 GLn-eigenvariety and a conjecture of Venkatesh ( pdf | journal ), with J. Thorne
Selecta Math., Vol. 23 Issue 2, pp. 1205-1234. A lecture at the IAS.

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 ( pdf | arxiv )
Preprint (version of 6/15/2016)

Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality ( pdf arxiv | journal )
J. reine angew. Math., Vol. 2017 Issue 730, pp. 1-64.

Minimal modularity lifting for GL2 over an arbitrary number fieldpdf arxiv )
Math. Res. Letters, to appear.

Shimura lifts of half-integral weight modular forms arising from theta functionspdf ), 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.

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

Smoothness of Bunn for dinguses (pdf )
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 (pdf )
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 (pdf )
Some version of this material will appear in "Iwasawa theory of overconvergent modular forms, II".

p-adic geometry, d'apres Peter Scholze (pdf )
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.

Don't be nervous

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