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Schur-finiteness (and bass-finiteness) conjecture for quadric fibrations and families of sextic du Val del Pezzo surfaces
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Tabuada, Gonçalo (2020) Schur-finiteness (and bass-finiteness) conjecture for quadric fibrations and families of sextic du Val del Pezzo surfaces. Documenta Mathematica . pp. 2339-2354. 25. doi:10.25537/dm.2020v25.2339-2354
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Official URL: https://doi.org/10.25537/dm.2020v25.2339-2354
Abstract
Let Q→B be a quadric fibration and T→B a family of sextic du Val del Pezzo surfaces. Making use of the theory of noncommutative mixed motives, we establish a precise relation between the Schur-finiteness conjecture for Q, resp. for T, and the Schur-finiteness conjecture for B. As an application, we prove the Schur-finiteness conjecture for Q, resp. for T, when B is low-dimensional. Along the way, we obtain a proof of the Schur-finiteness conjecture for smooth complete intersections of two or three quadric hypersurfaces. Finally, we prove similar results for the Bass-finiteness conjecture.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Schur functions, Quadrics, Surfaces, Algebraic, Noncommutative algebras | ||||||
| Journal or Publication Title: | Documenta Mathematica | ||||||
| Publisher: | Deutsche Mathematiker Vereinigung | ||||||
| ISSN: | 1431-0643 | ||||||
| Official Date: | 25 December 2020 | ||||||
| Dates: |
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| Page Range: | pp. 2339-2354 | ||||||
| Article Number: | 25 | ||||||
| DOI: | 10.25537/dm.2020v25.2339-2354 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access | ||||||
| RIOXX Funder/Project Grant: |
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