Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces

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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.

Original languageEnglish
Pages (from-to)2339-2354
Number of pages16
JournalDocumenta Mathematica
Volume25
DOIs
Publication statusPublished - 2020

Keywords

  • Bass-finiteness
  • conjecture
  • du Val del Pezzo surfaces
  • noncommutative algebraic geometry
  • noncommutative mixed motives
  • quadric fibrations
  • Schur-finiteness conjecture

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