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arXiv · 1603.01705

Syntomic cohomology and $p$-adic motivic cohomology

Veronika Ertl·Wieslawa Niziol
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Abstract

We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. It gives a description, in the stable range, of p-adic motivic cohomology (defined using algebraic cycles) in terms of differential forms. This generalizes a result of Geisser from small Tate twists to all twists and uses as a critical new ingredient the comparison theorem between syntomic complexes and p-adic nearby cycles proved recently in Colmez-Niziol.

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Veronika Ertl, Wieslawa Niziol. 2016-03-05. Syntomic cohomology and $p$-adic motivic cohomology. https://arxiv.org/abs/1603.01705

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