English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We define and study transversal weight and t-structures (for triangulated categories); if a weight structure is transversal to a t-one, then it defines certain ‘weights’ for its heart. Our results axiomatize and describe in detail the relations between the Chow weight structure wChow for Voevodsky’s motives (introduced in a preceding paper), the (conjectural) motivic t-structure, and the conjectural weight filtration for them. This picture becomes non-conjectural when restricted to the derived categories of Deligne’s 1-motives (over a smooth base) and of Artin-Tate motives over number fields. In particular, we prove that the ‘weights’ for Voevodsky’s motives (that are given by wChow) are compatible with those for 1-motives (that were ‘classically’ defined using a quite distinct method); this result is new. Weight structures transversal to the canonical t-structures also exist for the Beilinson’s D H̃p (the derived category of graded polarizable mixed Hodge complexes) and for the derived category of (Saito’s) mixed Hodge modules. We also study weight filtrations for the heart of t and (the degeneration of) weight spectral sequences. The corresponding relation between t and w is strictly weaker than transversality; yet it is easier to check, and we still obtain a certain filtration for (objects of) the heart of t that is strictly respected by morphisms. In a succeeding paper we apply the results obtained in order to reduce the existence of Beilinson’s mixed motivic sheaves (over a base scheme S) and ‘weights’ for them to (certain) standard motivic conjectures over a universal domain K.

Weight structures and “weights” on the hearts of $t$-structures