Orientation theory in arithmetic geometry - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2018

Orientation theory in arithmetic geometry

Résumé

This work is devoted to study orientation theory in arithmetic geometric within the motivic homotopy theory of Morel and Voevodsky. The main tool is a formulation of the absolute purity property for an \emph{arithmetic cohomology theory}, either represented by a cartesian section of the stable homotopy category or satisfying suitable axioms. We give many examples, formulate conjectures and prove a useful property of analytical invariance. Within this axiomatic, we thoroughly develop the theory of characteristic and fundamental classes, Gysin and residue morphisms. This is used to prove Riemann-Roch formulas, in Grothendieck style for arbitrary natural transformations of cohomologies, and a new one for residue morphisms. They are applied to rational motivic cohomology and \'etale rational $\ell$-adic cohomology, as expected by Grothendieck in \cite[XIV, 6.1]{SGA6}.

Dates et versions

hal-02357234 , version 1 (09-11-2019)

Identifiants

Citer

Frédéric Déglise. Orientation theory in arithmetic geometry. International Colloquium on K-theory, V. Srinivas, S. K. Roushon, Amalendu Krishna, A. J. Parameswaran, Ravi A. Rao, Jan 2016, Mumbai, India. ⟨hal-02357234⟩
45 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More