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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Mod p points on Shimura varieties of parahoric level

Pol Van Hoften
King's College London math department
https://nms.kcl.ac.uk/pol.van_hoften/

Date(s) : 01/04/2021   iCal
16h00 - 17h00

The conjecture of Langlands-Rapoport gives a conjectural description of the mod p points of Shimura varieties, with applications towards computing the (semi-simple) zeta function of these Shimura varieties. The conjecture was proven by Kisin for abelian type Shimura varieties at primes of (hyperspecial) good reduction, after having constructed smooth integral models. For primes of (parahoric) bad reduction, Kisin and Pappas have constructed a good integral model and the conjecture was generalised to this setting by Rapoport. In this talk I will discuss recent results towards the conjecture for these integral models, under minor hypothesis, building on earlier work of Zhou. Along the way we will see irreducibility results for various stratifications on special fibers of Shimura varieties, including irreducibility of central leaves and Ekedahl-Oort strata.

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