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
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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.
DOI : 10.4171/dm/800
Classification : 14A22, 14C15, 14D06
Mots-clés : noncommutative mixed motives, noncommutative algebraic geometry, Schur-finiteness conjecture, Bass-finiteness conjecture, quadric fibrations, du Val del Pezzo surfaces 
@article{10_4171_dm_800,
     author = {Gon\c{c}alo Tabuada},
     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},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/800},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/800/}
}
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Gonçalo Tabuada. 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. doi: 10.4171/dm/800

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