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Wiesława Nizioł

Publications and source records attributed to Wiesława Nizioł.

22 records · Page 2Linked to original sources
arXiv2019

Integral $p$-adic étale cohomology of Drinfeld symmetric spaces

We compute the integral $p$-adic étale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational $p$-adic étale cohomology from Colmez-Dospinescu-Nizioł. The main tools are: the computation of the integral de Rham cohomology from CDN and the integral $p$-adic comparison theorems of Bhatt-Morrow-Scholze and Česnavičius-Koshikawa which replace the quasi-integral comparison theorem of Tsuji used in CDN.

math.AG↗
arXiv2016

Syntomic cohomology and regulators for varieties over p-adic fields

We show that the logarithmic version of the syntomic cohomology of Fontaine and Messing for semistable varieties over $p$-adic rings extends uniquely to a cohomology theory for varieties over $p$-adic fields that satisfies $h$-descent. This new cohomology - syntomic cohomology - is a Bloch-Ogus cohomology theory, admits period map to étale cohomology, and has a syntomic descent spectral sequence (from an algebraic closure of the given field to the field itself) that is compatible with the Hochschild-Serre spectral sequence on the étale side. In relative dimension zero we recover the potentially semistable Selmer groups and, as an application, we prove that Soulé's étale regulators land in the potentially semistable Selmer groups. Our construction of syntomic cohomology is based on new ideas and techniques developed by Beilinson and Bhatt in their recent work on $p$-adic comparison

math.NT↗
arXiv2015

On $p$-adic absolute Hodge cohomology and syntomic coefficients, I

We interpret syntomic cohomology of Nekovář-Nizioł as a $p$-adic absolute Hodge cohomology. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomology by Beilinson and generalizes the results of Bannai and Chiarellotto, Ciccioni, Mazzari in the good reduction case, and of Yamada in the semistable reduction case. This interpretation yields a simple construction of the syntomic descent spectral sequence and its degeneration for proper and smooth varieties. We introduce syntomic coefficients and show that in dimension zero they form a full triangulated subcategory of the derived category of potentially semistable Galois representations. Along the way, we obtain $p$-adic realizations of mixed motives including $p$-adic comparison isomorphisms. We apply this to the motivic fundamental group generalizing results of Olsson and Vologodsky.

math.AG↗