P-adic Hodge Theory in Rigid Analytic Families

Download or read book P-adic Hodge Theory in Rigid Analytic Families written by Rebecca Michal Bellovin and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study p-adic Hodge theory in rigid analytic families. Roughly speaking, p-adic Hodge theory is the study of p-adic representations of p-adic Galois groups. One introduces certain p-adic period rings B, such as B_{HT}, B_{dR}, B_{st}, and B_{cris}, and uses them to define functors D_B(.) from the category of p-adic Galois representations to various categories of linear algebra data. In the first half of this thesis, we study generalizations of these functors to families of p-adic Galois representations with rigid analytic coefficients. We prove that the functors D_{HT}(.) and D_{dR}(.) are coherent sheaves, and we prove that the B-admissible locus is a closed subspace of the base. In the second half of this thesis, we study the linear algebra data which arises from families of potentially semi-stable Galois representations valued in a connected reductive group G. We prove that for any G, the moduli space of linear algebra data is reduced and locally a complete intersection, and we deduce that potentially semi-stable deformation rings are generically smooth and equi-dimensional.