Generators of top cohomology
Manoj Kummini, Mohit Upmanyu

TL;DR
This paper constructs explicit generators for the top cohomology of certain smooth proper morphisms over specific rings, extending classical duality results and addressing a question by Lipman.
Contribution
It provides explicit exact sequences generating top cohomology modules in new cases, including DVRs with sections and Grassmannians over integers.
Findings
Generated top cohomology modules explicitly in new cases.
Connected classical duality with explicit generators.
Partially answered Lipman's question.
Abstract
Let be a commutative noetherian ring and a proper smooth morphism, of relative dimension . From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map is an isomorphism when has geometrically connected fibres. We construct an exact sequence that generates as an -module in the following cases: (1) when is a DVR and has a section; (2) when and is the Grassmannian for some . This partially answers a question raised by Lipman.
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
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Advanced Topics in Algebra
