The specialization principle for p-adic kimberlites, I

Speaker:

Ian Gleason

Organiser(s):

Peter Scholze

Zugehörigkeit:

Universität Bonn

Datum:

Don, 04/11/2021 - 12:00 - 14:00

Parent event:

Arbeitsgemeinschaft Arithmetische Geometrie [2]

Attendance for max. 20 MPIM guests (2G) in the MPIM lecture hall. For everyone else participation via Zoom only!
For zoom details please contact Peter Scholze (scholze@mpim-bonn.mpg.de).

In his master thesis Lourenço proposes and proves a specialization principle for certain formal schemes. Roughly speaking, this says that a formal scheme can be recovered from its special fiber, its rigid generic fiber and the specialization map. Kimberlites were introduced by the speaker as analogues of formal schemes in Scholze's theory of v-sheaves. In forthcoming joint work with Anschütz, Lourenço and Richarz we prove a similar specialization principle for p-adic kimberlites. This result is a key step of our proof of the Scholze-Weinstein conjecture on local models of Shimura varieties.

Talk 1:

-We summarize the main concepts and constructions of the theory of kimberlites.

Talk 2:

-We prove the specialization principle. We prove that bounded parahoric B_dR Grassmanians satisfy the hypothesis of the specialization principle.