TL;DR
This paper develops a new formulation of Tate cohomology within three functor formalisms, establishing key properties and extending its applicability to various mathematical contexts.
Contribution
It introduces a generalized definition of Tate cohomology and proves foundational properties using a framework inspired by Nikolaus-Scholze's approach.
Findings
Established monoidality and functoriality of Tate cohomology
Extended Tate cohomology to new mathematical settings
Provided a unified formalism for Tate cohomology
Abstract
We formulate a definition of Tate cohomology in the context of three functor formalisms, and we establish basic monoidality and functoriality properties of it in this context. Our approach to these properties is based on the treatment of Nikolaus-Scholze in the setting of local systems of spectra on spaces. We discuss a couple of other specific settings of interest that are accommodated by our generalization.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory