Semistable periods of finite slope families

TL;DR

This paper introduces finite slope families to study p-adic Galois representations and proves the analytic continuation of semi-stable and crystalline periods within these families.

Contribution

It defines finite slope families and establishes the analytic continuation of semi-stable and crystalline periods for these families.

Findings

Finite slope families effectively encode local properties of p-adic Galois representations.

Proved the analytic continuation of semi-stable periods in these families.

Extended the understanding of p-adic Galois representations in automorphic contexts.

Abstract

We introduce the notion of finite slope families to encode the local properties of the p-adic families of Galois representations appearing in the work of Harris, Lan, Taylor and Thorne on the construction of Galois representations for (non-self dual) regular algebraic cuspidal automorphic representations of GL(n) over CM fields. Our main result is to prove the analytic continuation of semi-stable (and crystalline) periods for such families.