p-adic Hodge theory in rigid analytic families

Bellovin, R. (2015) p-adic Hodge theory in rigid analytic families. Algebra and Number Theory, 9(2), pp. 371-433. (doi: 10.2140/ant.2015.9.371)

Abstract

We study the functors DB∗(V), where B∗ is one of Fontaine’s period rings and V is a family of Galois representations with coefficients in an affinoid algebra A. We first relate them to (φ,Γ)-modules, showing that DHT(V)=⊕i∈Z(DSen(V)⋅ti)ΓK, DdR(V)=Ddif(V)ΓK, and Dcris(V)=Drig(V)[1∕t]ΓK; this generalizes results of Sen, Fontaine, and Berger. We then deduce that the modules DHT(V) and DdR(V) are coherent sheaves on Sp(A), and Sp(A) is stratified by the ranks of submodules D[a,b]HT(V) and D[a,b]dR(V) of “periods with Hodge–Tate weights in the interval [a,b]@”. Finally, we construct functorial B∗-admissible loci in Sp(A), generalizing a result of Berger and Colmez to the case where A is not necessarily reduced.

• Item Type: Articles
• Additional Information: This work was partially supported by an NSF Graduate Research Fellowship.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellovin, Dr Rebecca
• Authors: Bellovin, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebra and Number Theory
• Publisher: Mathematical Sciences Publishers (MSP)
• ISSN: 1937-0652
• ISSN (Online): 1944-7833