Weight structures and motives; comotives, coniveau and Chow-weight spectral sequences, and mixed complexes of sheaves: a survey

Abstract

This is a survey of author's results on weight structures and Voevodsky's motives. Weight structures are natural counterparts of t-structures (for triangulated categories) introduced by the author. They allow to construct weight complexes, weight filtrations, and weight spectral sequences for various cohomology theories. Partial cases of the latter are: 'classical' weight spectral sequences (for singular and etale cohomology), coniveau spectral sequences, and Atiyah-Hirzebruch spectral sequences. All of those are mentioned in the current paper. The details, proofs, and several more results could be found in other papers of the author (cited here). We also mention a certain triangulated category of comotives that contains reasonable (co)motives for all function fields (and also of other projective limits of smooth varieties).

Several minor corrections made

References in corpus (1)

• Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields

Cited by in corpus (5)

• On exact categories and applications to triangulated adjoints and model structures
• A geometric construction of colored HOMFLYPT homology
• Weights for relative motives; relation with mixed complexes of sheaves
• On compactly generated torsion pairs and the classification of co-t-structures for commutative noetherian rings
• Weights and t-structures: in general triangulated categories, for 1-motives, mixed motives, and for mixed Hodge complexes and modules