The London-Paris Number Theory Seminar meets twice per year, once in London and once in Paris. It is supported by grants from ANR Projet ArShiFo ANR-BLAN-0114, EPSRC Platform Grant EP/I019111/1, PerCoLaTor (Grant ANR-14-CE25), the Heilbronn Institute for Mathematical Research, and ERC Advanced Grant AAMOT.

London organizers: Kevin Buzzard, Ana Caraiani, Fred Diamond, Vladimir Dokchitser, Yiannis Petridis, Sarah Zerbes.

Paris organizers: Olivier Fouquet, Michael Harris, Marc Hindry, Matthew Morrow, Jacques Tilouine.

The 26th meeting of the LPNTS will take place at King's College London. The theme is p-adic cohomology and integration.

Dates: 7th to 8th May.

Location: King's College London.

Lectures: Anatomy Lecture Theatre (K6.29), King’s Building

Tuesday coffees: the adjoining Anatomy Museum

Wednesday coffee: S5.20

Schedule:

Tuesday 7th May

11:00 Welcome/coffee

11:30 Jennifer Balakrishnan

12:30 Lunch

14:00 Netan Dogra

15:00 Veronika Ertl

16:00 Coffee

16:30 Wieslawa Niziol

Wednesday 8th May

10:00 Johannes Anschutz

11:00 Coffee

11:30 Andreas Langer

Titles and abstracts:

Jennifer Balakrishnan

Title: Explicit p-adic integration on curves.

Abstract: I will give a survey of some recent algorithms for p-adic (Coleman) integration on curves, including work of Best, Bianchi, and Tuitman. I will further describe applications concerning p-adic heights and computing rational points on curves.

Netan Dogra

Title: The Chabauty-Kim method at a prime of bad reduction.

Abstract: The Chabauty-Kim method uses p-adic integration, in the guise of a Frobenius action and Hodge filtration on fundamental groupoids, to determine rational points on curve. In my talk I will describe joint work in progress with Jan Vonk making this explicit and computable in the case where p is a prime of bad reduction for the curve. I will also discuss work with Alex Betts describing the information contained in the monodromy action on the fundamental groupoid.

Veronika Ertl

Title: Comparison of crystalline syntomic and rigid syntomic cohomology for strictly semistable schemes.

Abstract: We prove a comparison isomorphism between Nekovár and Nizioł's syntomic cohomology and log rigid syntomic cohomology for a strictly semistable scheme with a nice compactification. Key points are a generalization of Große-Klönne's log rigid cohomology and the compatibility of crystalline and rigid Hyodo-Kato maps on the Frobenius eigenspaces.

This is joint work with Kazuki Yamada.

Wieslawa Niziol

Title: Integral p-adic cohomology of Drinfeld half-spaces.

Abstract: I will compute the integral p-adic etale cohomology of Drinfeld half-spaces of any dimension. This refines the existing computation of the rational p-adic etale cohomology. The main tools are: the computation of the integral de Rham cohomology and the integral p-adic comparison theorems of Bhatt-Morrow-Scholze and Cesnavicius-Koshikawa which replace the quasi-integral comparison theorem of Tsuji used to compute the rational etale cohomology. This is a joint work with Colmez and Dospinescu.

Johannes Anschutz

Title: Prismatic Dieudonne theory

Abstract: Building on the theory of prismatic cohomology which was recently
introduced by Bhatt and Scholze we want to present the definition of a
prismatic Dieudonne functor over p-completely quasi-syntomic rings and
explain how to use it to obtain a classification of p-divisible groups
over such rings by a generalization of minuscule Breuil-Kisin(-Fargues) modules.

This is joint work with Arthur-Cesar Le Bras.

Andreas Langer

Title: Relative de Rham-Witt cohomology and applications to p-adic deformation theory .

Abstract: In my talk I will describe new results on the relative de Rham-Witt complex and its Nygaard filtration and then discuss two applications: one is a relative version of p-adic deformation theory of algebraic cycles due to Bloch/Esnault/Kerz; the other is a construction of higher Displays and a crystal of relative Displays for a class of smooth projective schemes satisfying some general assumptions.

Previous meetings:

21st meeting (Jussieu, 14--15/11/16)

22nd meeting (UCL, 5--6/6/17)

23rd meeting (Jussieu, 27--28/11/17)

24th meeting (UCL, 29--30/5/18)

25th meeting (Jussieu, 26--27/11/18)

This page is maintained by Kevin Buzzard.