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The rigid syntomic ring spectrum

Authors
  • Déglise, Frédéric
  • Mazzari, Nicola
Type
Published Article
Publication Date
Jun 10, 2014
Submission Date
Nov 21, 2012
Identifiers
DOI: 10.1017/S1474748014000152
Source
arXiv
License
Yellow
External links

Abstract

The aim of this paper is to show that Besser syntomic cohomology 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 syntomic cohomology such as h-descent and the compatibility of cycle classes with Gysin morphisms. Along the way, we prove that motivic ring spectra induces a complete Bloch-Ogus cohomological formalism and even more. Finally, following a general motivic homotopical philosophy, we exhibit a natural notion of syntomic coefficients.

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