Invariants birationnels dans la suite spectrale de Bloch-Ogus

TL;DR

This paper proves that certain E_2-terms of the Bloch-Ogus spectral sequence are birational invariants for smooth projective varieties over fields of finite cohomological dimension, linking them to cycle class maps over finite fields.

Contribution

It establishes the birational invariance of specific E_2-terms in the Bloch-Ogus spectral sequence and relates them to cycle class maps over finite fields.

Findings

Certain E_2-terms are birational invariants.

Over finite fields, these invariants relate to the cokernel of the l-adic cycle class map.

Provides new connections between spectral sequence invariants and cycle maps.

Abstract

For a field k of cohomological dimension d we prove that some E_2-terms of the Bloch-Ogus spectral sequence are birational invariants of smooth projective geometrically integral varieties over k. Over a finite field, we relate one of these invariants with the cokernel of the l-adic cycle class map for 1-cycles. Soit k un corps de dimension cohomologique d. On \'etablit que certains E_2-termes de la suite spectrale de Bloch-Ogus sont des invariants birationnels des k-vari\'et\'es projectives et lisses, g\'eom\'etriquement int\`egres. Sur un corps fini, on relie un de ces invariants au conoyau de l'application classe de cycle l-adique \'etale pour les 1-cycles.