p-adic K-theory of p-adic rings

12 juin 2018, 11:45
1h
Centre de Conférences Marilyn et James Simons (Le Bois-Marie)

Centre de Conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Orateur

P. Scholze (Universität Bonn)

Description

The original proof of Grothendieck's purity conjecture in étale cohomology (the Thomason-Gabber theorem) relies on results on l-adic K-theory and its relation to étale cohomology when l is invertible. Using recent advances of Clausen-Mathew-Morrow and joint work with Bhatt and Morrow, our understanding in the complementary case of p-adic K-theory of p-adic rings has reached a similar level. In particular, we can express p-adic étale K-theory in terms of the cohomology theories of integral p-adic Hodge theory, such as the prismatic cohomology discussed in Bhatt's talk. Depending on time, I may indicate some possible applications.

Documents de présentation