Structures de poids \`a la Bondarko sur les motifs de Beilinson

TL;DR

This paper extends Bondarko's weight structure from Voevodsky motives to Beilinson motives over schemes of finite type, broadening the applicability of weight structures in motivic categories.

Contribution

The authors generalize the weight structure to Beilinson motives over schemes of finite type, expanding the framework beyond Voevodsky motives.

Findings

Weight structure successfully extended to Beilinson motives.

Applicable over schemes of finite type over excellent schemes of dimension at most two.

Enhances understanding of motivic categories and their structures.

Abstract

In [Bon07], Bondarko defines and studies the notion of weight structure and he shows that there exist a weight structure over the category of Voevodsky motives with rationals coefficients (over a field of characteristic 0). In this paper we extend this weight structure to the category of Beilinson motives (for any scheme of finite type over a base scheme which is excelent of dimension at most two) introduced and studied by Cisinsky-D\'eglise. ----- Dans [Bon07], Bondarko d\'efinit et \'etudie la notion de structure de poids et il montre qu'il existe une structure de poids sur la cat\'egorie des motifs de Voevodsky \`a coefficients rationnels (sur un corps de caract\'eristique 0). Dans cet article nous \'etendons cette structure de poids \`a la cat\'egorie des motifs de Beilinson (pour un sch\'ema de type fini sur un sch\'ema de base qui est excellent de dimension au plus deux) introduite et \'etudi\'ee par Cisinsky-D\'eglise ([CD09]).