Interpolating Hodge-Tate and de Rham Periods

Abstract

We study the interpolation of Hodge-Tate and de Rham periods over rigid analytic families of Galois representations. Given a Galois representation on a coherent locally free sheaf over a reduced rigid space and a bounded range of weights, we obtain a stratification of this space by locally closed subvarieties where the Hodge-Tate and bounded de Rham periods (within this range) as well as 1-cocycles form locally free sheaves. We also prove strong vanishing results for higher cohomology. Together, these results give a simultaneous generalization of results of Sen, Kisin, and Berger-Colmez. The main result has been applied by Varma in her proof of geometricity of Harris-Lan-Taylor-Thorne Galois representations as well as in several works of Ding.

Final version. To appear in Res. Math. Sci

References in corpus (4)

• $p$-adic Hodge theory in rigid analytic families
• The Eigencurve is Proper
• Semistable periods of finite slope families
• Companion points and locally analytic socle for ${\mathrm{GL}}_2(L)$

Cited by in corpus (5)

• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• On some partially de Rham Galois representations
• $\mathcal{L}$-invariants and local-global compatibility for the group ${\mathrm{GL}}_2/F$
• Companion points and locally analytic socle for ${\mathrm{GL}}_2(L)$
• The Chabauty-Kim Method for Relative Completions