The first obstructions to enhancing a triangulated category
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-019-02438-y
Abstract: In this paper we relate triangulated category structures to the cohomology of small categories and define initial obstructions to the existence of an algebraic or topological enhancement. We show that these obstructions do not vanish… read more here.
Keywords: category; enhancing triangulated; obstructions enhancing; triangulated category ... See more keywords
Purity of reciprocity sheaves
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2020.107067
Abstract: The purpose of this paper is to prove a conjecture on reciprocity sheaves by Kahn-Saito-Yamazaki. This is accomplished by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalizations, reciprocity sheaves and… read more here.
Keywords: reciprocity sheaves; triangulated category; purity reciprocity; reciprocity ... See more keywords
On cluster-tilting objects in a triangulated category with Serre duality
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Algebra"
DOI: 10.1080/00927872.2016.1214273
Abstract: ABSTRACT Let ???? be a Krull–Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object T. We introduce the notion of an FΛ-stable support τ-tilting module, induced by the shift functor and the… read more here.
Keywords: tilting objects; cluster tilting; category serre; triangulated category ... See more keywords