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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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Resumo(s)
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.
Descrição
The author is grateful to Joseph Ayoub for useful e-mail exchanges concerning the Schur-finiteness conjecture, and to the anonymous referee for her/his comments and for suggesting Remark 10. The author also would like to thank the Hausdorff Institute for Mathematics (HIM) in Bonn for its hospitality.
Palavras-chave
Bass-finiteness conjecture du Val del Pezzo surfaces noncommutative algebraic geometry noncommutative mixed motives quadric fibrations Schur-finiteness conjecture General Mathematics