Abstract: Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles, introduced by Hitchin more than 35 years ago. Starting with the case in which G is the circle, and the 19th century Abel-Jacobi's theory, we will move to the case of G=SL(2,R) and the relation to Teichmüller t...
Description:The first half of this course gives a general introduction to p-adic Hodge theory. The second part discusses recent topics, including the Fargues-Fontaine curve and p-adic period domains.Prerequisite:Algebraic number theory and algebraic geometryReference:Laurent Fargues and Jean-Marc Fontaine. Courbes et fibrés vectoriels en théorie de Hodge p-adique. Astérisque (406).Jean-Franç...