The rigid syntomic ring spectrum
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.
Keywords
Cite
@article{arxiv.1211.5065,
title = {The rigid syntomic ring spectrum},
author = {Frédéric Déglise and Nicola Mazzari},
journal= {arXiv preprint arXiv:1211.5065},
year = {2015}
}
Comments
Final version to appear in the Journal de l'institut des Math\'ematiques de Jussieu. Many typos have been corrected and the exposition has been improved according to the suggestions of the referees: we thank them a lot!