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The rigid syntomic ring spectrum
Language
en
Article de revue
This item was published in
Journal of the Institute of Mathematics of Jussieu. 2015-10-01, vol. 14, n° 4, p. p. 1-47
Cambridge University Press (CUP)
English 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 ...Read more >
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.Read less <
English Keywords
Rigid syntomic cohomology
Beilinson motives
Bloch-Ogus
Origin
Hal imported