A generalization of Coleman's 
p-adic integration theory
(Final version, to appear in Inventiones)

coleman.ps.gz
(195k, unpack using gunzip) Amnon Besser E-mail: bessera@math.bgu.ac.il URL: http://www.cs.bgu.ac.il/~bessera/
We associate to a scheme X smooth over a p-adic ring a kind of cohomology group H_fpⁱ(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 $H_{syn}^{2i}(X,i)\hookrightarrow H_{fp}^{2i}(X,i)$ 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.
 

1999-02-14