Hodge theory of $p$-adic varieties: a survey
Volume 127 / 2021
Annales Polonici Mathematici 127 (2021), 63-86
MSC: 11G25.
DOI: 10.4064/ap200516-31-8
Published online: 15 December 2020
Abstract
$p$-adic Hodge theory is one of the most powerful tools in modern arithmetic geometry. In this survey, we will review $p$-adic Hodge theory of algebraic varieties, present current developments in $p$-adic Hodge theory of analytic varieties, and discuss some of its applications to problems in number theory. This is an extended version of a talk at the Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Kraków, 2019.
