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Local Points of Motives in Semistable Reduction

Published online by Cambridge University Press:  04 December 2007

ANDREAS LANGER
Affiliation:
Mathematisches Institut der Universität Münster, Einsteinster. 62, D-48149 M¨nster Germany; e-mail: [email protected]
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Abstract

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In this paper we study – for a semistable scheme – a comparison map between its log-syntomic cohomology and the p-adic étale cohomology of its generic fiber. The image can be described in terms of what Bloch and Kato call the local points of the underlying motive. The results extend a proven conjecture of Schneider which treats the good reduction case. The proof uses the theory of logarithmic schemes, some crystalline cohomology theories defined on them and various techniques in p-adic Hodge theory, in particular the Fontaine–Jannsen conjecture proven by Kato and Tsuji as well as Fontaine‘s rings of p-adic periods and their properties. The comparison result may become useful with respect to cycle class maps.

Type
Research Article
Copyright
© 1999 Kluwer Academic Publishers