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Journal Articles Commentarii Mathematici Helvetici Year : 2018

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

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Frédéric Déglise
Wieslawa Niziol
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Abstract

We interpret syntomic cohomology defined in [49] as a p-adic absolute Hodge cohomology. This is analogous to the interpretation of Deligne-Beilinson cohomology as an absolute Hodge cohomol-ogy by Beilinson [8] and generalizes the results of Bannai [6] and Chiarellotto, Ciccioni, Mazzari [15] in the good reduction case. This interpretation yields a simple construction of the syntomic descent spectral sequence and its degeneration for projective 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 isomor-phisms. We apply this to the motivic fundamental group generalizing results of Olsson and Vologodsky [55], [69].
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ensl-01420349 , version 1 (20-12-2016)

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Frédéric Déglise, Wieslawa Niziol. On p-adic absolute Hodge cohomology and syntomic coefficients, I.. Commentarii Mathematici Helvetici, 2018, 93 (1), pp.71-131. ⟨10.4171/CMH/430⟩. ⟨ensl-01420349⟩
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