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:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
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.
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
SN - 1431-0635
VL - 25
SP - 2339
EP - 2354
JO - Documenta Mathematica
JF - Documenta Mathematica
ER -