Abstract
We study the functors , where is one of Fontaine’s period rings and is a family of Galois representations with coefficients in an affinoid algebra . We first relate them to -modules, showing that , , and ; this generalizes results of Sen, Fontaine, and Berger. We then deduce that the modules and are coherent sheaves on , and is stratified by the ranks of submodules and of “periods with Hodge–Tate weights in the interval ”. Finally, we construct functorial -admissible loci in , generalizing a result of Berger and Colmez to the case where is not necessarily reduced.
Citation
Rebecca Bellovin. "$p$-adic Hodge theory in rigid analytic families." Algebra Number Theory 9 (2) 371 - 433, 2015. https://doi.org/10.2140/ant.2015.9.371
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