On Galois equivariance of homomorphisms between torsion potentially crystalline representations

Abstract

Let K be a complete discrete valuation field of mixed characteristic (0,p) with perfect residue field. Let (π_n)_{n\ge 0} be a system of p-power roots of a uniformizer π=π_0 of K with π^p_{n+1}=π_n, and define G_s (resp.\ G_{\infty}) the absolute Galois group of K(π_s) (resp.\ K_{\infty}:=\bigcup_{n\ge 0} K(π_n)). In this paper, we study G_s-equivatiantness properties of G_{\infty}-equivariant homomorphisms between torsion (potentially) crystalline representations

arXiv comment29 pages, some arguments are generalized, Theorem 4.16 is added

References in corpus (2)

• Group schemes of period 2
• Full faithfulness theorem for torsion crystalline representations

Cited by in corpus (1)

• Lattices in potentially semi-stable representations and weak $(\phi ,\hat{G})$-modules