Self cup products and the theta characteristic torsor
Bjorn Poonen, Eric Rains
TL;DR
This paper establishes a general formula linking self cup products in cohomology to nonabelian cohomology connecting maps, and applies it to derive a formula related to the Weil pairing's self cup product.
Contribution
It introduces a unified approach to relate cohomological cup products with nonabelian cohomology, providing new formulas for specific pairings.
Findings
Derived a formula connecting self cup products to nonabelian cohomology maps
Applied the formula to obtain a new expression for the Weil pairing's self cup product
Enhanced understanding of the algebraic structure of cohomological pairings
Abstract
We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.
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.