Time: 10:30-11:30 Xu Shen (CAS), 2:00-3:00 Xin Wan (CAS), 3:15-4:15 Laurent Fargues (CNRS)

Xu Shen:

Title: Harder-Narasimhan strata and p-adic period domains

Abstract: We revisit the Harder-Narasimhan stratification on a p-adic flag variety by the theory of modifications of G-bundles on the Fargues-Fontaine curve. This allows us to compare the Harder-Narasimhan strata with the Newton strata introduced by Caraiani-Scholze. As a consequence, we get further equivalent conditions in terms of p-adic Hodge-Tate period domains for fully Hodge-Newton decomposable pairs.

Xin Wan:

Title: Iwasawa theory and Bloch-Kato conjecture for unitary groups

Abstract: We present a new approach to study Iwasawa theory and Eisenstein congruences on unitary groups of general signature over CM fields. As a consequence we prove that if the central L-value vanishes at a point, then the corresponding Selmer group has rank at least 1. This generalizes a result of Skinner-Urban in 2006 ICM report.

Laurent Fargues:

Title: A minimality property for integral models of Rapoport Zink spaces

Abstract: Rapoport and Zink have defined moduli spaces of p-divisible groups. Those are formally smooth formal schemes whose generic fiber is a rigid analytic space. We prove that those formal schemes are "minimal models" of their generic fiber.