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SYNTOMIC COHOMOLOGY AND p-ADIC MOTIVIC COHOMOLOGY

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 [10] 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 [8].
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Submitted on : Tuesday, December 20, 2016 - 2:39:00 PM
Last modification on : Tuesday, November 19, 2019 - 10:34:40 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 1:17:57 AM

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Veronika Ertl, Wieslawa Niziol. SYNTOMIC COHOMOLOGY AND p-ADIC MOTIVIC COHOMOLOGY. Algebraic Geometry, Foundation Compositio Mathematica, In press. ⟨ensl-01420347⟩

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