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

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].
Liste complète des métadonnées

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01420349
Contributor : Wieslawa Niziol <>
Submitted on : Tuesday, December 20, 2016 - 2:41:14 PM
Last modification on : Thursday, February 7, 2019 - 5:15:47 PM
Document(s) archivé(s) le : Tuesday, March 21, 2017 - 8:46:27 AM

File

avec-fred12.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-01420349, version 1

Citation

Frédéric Déglise, Wieslawa Niziol. On p-adic absolute Hodge cohomology and syntomic coefficients, I.. Commentarii Mathematici Helvetici, European Mathematical Society, 2018. ⟨ensl-01420349⟩

Share

Metrics

Record views

177

Files downloads

77