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THE RIGID SYNTOMIC RING SPECTRUM

Part of: (Co)homology theory

Published online by Cambridge University Press:  13 June 2014

F. Déglise  and
N. Mazzari
F. Déglise
Affiliation:
ENS de Lyon, France ([email protected])
N. Mazzari
Affiliation:
Université de Bordeaux, France ([email protected])
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Abstract

The aim of this paper is to show that rigid syntomic cohomology – defined by Besser – is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous constructions, we exhibit a simple representability criterion and we apply it to several cohomologies in order to get our central result. This theorem gives new results for rigid syntomic cohomology such as h-descent and the compatibility of cycle classes with Gysin morphisms. Along the way, we prove that motivic ring spectra induce a complete Bloch–Ogus cohomological formalism and even more. Finally, following a general motivic homotopical philosophy, we exhibit a natural notion of rigid syntomic coefficients.

Keywords

Rigid syntomic cohomologyBeilinson motivesBloch–Ogus

MSC classification

Primary: 14F42: Motivic cohomology; motivic homotopy theory 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 4 , October 2015 , pp. 753 - 799
Copyright
© Cambridge University Press 2014 

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