Geodesic
Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
Documenta mathematica, Tome 25 (2020), pp. 2339-2354.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $Q \to B$ be a quadric fibration and $T \to B$ 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.
Classification : 14A22, 14C15, 14D06
Keywords: Schur-finiteness conjecture, Bass-finiteness conjecture, quadric fibrations, du Val del Pezzo surfaces, noncommutative algebraic geometry, noncommutative mixed motives 
@article{DOCMA_2020__25__a7,
     author = {Tabuada, Gon\c{c}alo},
     title = {Schur-Finiteness (and {Bass-Finiteness)} {Conjecture} for {Quadric} {Fibrations} and {Families} of {Sextic} du {Val} del {Pezzo} {Surfaces}},
     journal = {Documenta mathematica},
     pages = {2339--2354},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a7/}
}
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Tabuada, Gonçalo. Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces. Documenta mathematica, Tome 25 (2020), pp. 2339-2354. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a7/