Hodge--Tate prismatic crystals and Sen theory
We study Hodge--Tate crystals on the absolute (log-) prismatic site of $\mathcal {O} _K $,
where $\mathcal {O} _K $ is a mixed characteristic complete discrete valuation ring with
perfect residue field. We first classify Hodge--Tate crystals by $\mathcal {O} _K $-modules
equipped with certain small endomorphisms. We then construct Sen theory over a non-
Galois Kummer tower, and use it to classify rational Hodge--Tate crystals by (log-) nearly
Hodge--Tate representations. Various cohomology comparison and vanishing results are …
where $\mathcal {O} _K $ is a mixed characteristic complete discrete valuation ring with
perfect residue field. We first classify Hodge--Tate crystals by $\mathcal {O} _K $-modules
equipped with certain small endomorphisms. We then construct Sen theory over a non-
Galois Kummer tower, and use it to classify rational Hodge--Tate crystals by (log-) nearly
Hodge--Tate representations. Various cohomology comparison and vanishing results are …
We study Hodge--Tate crystals on the absolute (log-) prismatic site of , where is a mixed characteristic complete discrete valuation ring with perfect residue field. We first classify Hodge--Tate crystals by -modules equipped with certain small endomorphisms. We then construct Sen theory over a non-Galois Kummer tower, and use it to classify rational Hodge--Tate crystals by (log-) nearly Hodge--Tate representations. Various cohomology comparison and vanishing results are proved along the way.
arxiv.org
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