Hodge Theory of p-adic varieties: a survey

2020/05/16 by Nizioł, Wiesaława
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.07919

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 for algebraic varieties, present current developments in p-adic Hodge Theory for 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.

Related

• Some new directions in p-adic Hodge theory
• p-adic geometry
• p-adic cohomology
• Hodge theory, between algebraicity and transcendence
• Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice