#### Vol. 9, No. 2, 2015

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Semistable periods of finite slope families

### Ruochuan Liu

Vol. 9 (2015), No. 2, 435–458
##### 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 $GL\left(n\right)$ over CM fields. Our main result is to prove the analytic continuation of semistable (and crystalline) periods for such families.

##### Keywords
finite slope families, semistable, $(\varphi,\Gamma)$-modules
Primary: 11F80