Poincar\'e Duality in abstract 6-functor formalisms
Bogdan Zavyalov
TL;DR
This paper explores Poincaré Duality within abstract 6-functor frameworks, providing minimal assumptions for its validity and offering new, formal proofs of existing results.
Contribution
It introduces a concise set of conditions that guarantee Poincaré Duality and applies these to produce uniform proofs of known duality theorems.
Findings
Minimal assumptions for Poincaré Duality established
New uniform proofs of existing duality results provided
Framework simplifies understanding of duality in abstract settings
Abstract
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal) proofs of some previously established Poincar\'e Duality results.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry