Abstract.
We associate to a scheme X smooth over a p-adic ring a kind of cohomology group H i fp (X,j). For proper X this cohomology has Poincaré duality hence Gysin maps and cycle class maps which are reasonably explicit. For zero-cycles we show that the cycle class map is given by Coleman integration. The cohomology theory H fp is therefore interpreted as giving a generalization of Coleman’s theory. We find an embedding H syn 2i (X,i)↪H fp 2i (X,i) where H syn is (rigid) syntomic cohomology. Our main result is an explicit description of the syntomic Abel-Jacobi map in terms of generalized Coleman integration.
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Oblatum 2-III-1999 & 11-IV-2000¶Published online: 16 August 2000
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Besser, A. A generalization of Coleman’s p-adic integration theory. Invent. math. 142, 397–434 (2000). https://doi.org/10.1007/s002220000093
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DOI: https://doi.org/10.1007/s002220000093