caa a22 4500 475738721 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1007/s002220000093 doi (NATIONALLICENCE)springer-10.1007/s002220000093 Besser Amnon SFB 478, Geometrische Strukturen in der Mathematik, Hittorfstr 27, 48149 Münster, Germany, DE aut A generalization of Coleman's p-adic integration theory [Elektronische Daten] [Amnon Besser] 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. Springer-Verlag Berlin Heidelberg, 2000 https://doi.org/10.1007/s002220000093 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220000093 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Besser Amnon SFB 478, Geometrische Strukturen in der Mathematik, Hittorfstr 27, 48149 Münster, Germany, DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer