Diamonds and p-adic period domains

Abstract: The theory of diamonds was introduced by Scholze in his 2014 Berkeley lectures, which provides a powerful tool to study p-adic Hodge theory and the Langlands program. In this talk, we will investigate the geometry of some diamonds, namely the B_{dR}^+-affine Schubert varieties, via the Fargues-Fontaine curve. Along the way, the theory of p-adic period domains arises naturally. We will explain how the de Rham periods and the Hodge-Tate periods are related to each other, and we will discuss the structure of certain generalized p-adic period domains.

Mathematics

Audience: researchers in the topic

ICCM 2020