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THE RIGID SYNTOMIC RING SPECTRUM

Published online by Cambridge University Press:  13 June 2014

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

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.

Type
Research Article
Copyright
© Cambridge University Press 2014 

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