TY - JOUR
T1 - Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
AU - Tabuada, Gonçalo
N1 - Funding Information:
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. The author was partially supported by the Fundacão para a Ciência e a Tecnolo-gia (Portuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matemática e Aplica¸cões).
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Bass-finiteness
KW - conjecture
KW - du Val del Pezzo surfaces
KW - noncommutative algebraic geometry
KW - noncommutative mixed motives
KW - quadric fibrations
KW - Schur-finiteness conjecture
UR - http://www.scopus.com/inward/record.url?scp=85099564782&partnerID=8YFLogxK
U2 - 10.25537/dm.2020v25.2339-2354
DO - 10.25537/dm.2020v25.2339-2354
M3 - Article
AN - SCOPUS:85099564782
VL - 25
SP - 2339
EP - 2354
JO - Documenta Mathematica
JF - Documenta Mathematica
SN - 1431-0635
ER -