Perfectoid空間論の整数論への応用 (Algebraic Number Theory and Related Topics 2014)

Abstract

We give a brief survey on number theoretic applications of the theory of perfectoid spaces recently obtained by Peter Scholze and his collaborators. We explain basic strategies and some ideas of the proofs of the weight-monodromy conjecture for complete intersections, comparison theorems for torsion coefficients for rigid analytic varieties, and the construction of Galois representations associated with regular algebraic cuspidal automorphic representations of GLn over totally real or CM fields as well as torsion cohomology classes of locally symmetric varieties. In this paper, no new results are given, and most of the arguments explained are only briefly sketched.