SYNTOMIC COHOMOLOGY AND p-ADIC MOTIVIC COHOMOLOGY

Veronika Ertl (1) , Wieslawa Niziol (2)

1 UR - Universität Regensburg
2 ENS Lyon - École normale supérieure - Lyon

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].

Domains: Mathematics [math]; Number Theory [math.NT]; Mathematics [math]; Algebraic Geometry [math.AG]

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