2018/01/13 by Yehonatan Sella, Sella, Yehonatan
Mathematics · #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1801.04450
openalex publication_date 2018/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This thesis is concerned with the mixed Tate property of reductive algebraic groups G, which in particular guarantees a Chow Kunneth property for the classifying space BG. Toward this goal, we first refine the construction of the compactly supported motive of a quotient stack. In the first section, we construct the compactly supported motive Mc(X) of an algebraic space X and demonstrate that it satisfies expected properties, following closely Voevodsky's work in the case of schemes. In the second section, we construct a functorial version of Totaro's definition of the compactly supported motive Mc([X/G]) for any quotient stack [X/G] where X is an algebraic space and G is an affine group scheme acting on it. A consequence of functoriality is a localization triangle for these motives. In the third section, we study the mixed Tate property for the classical groups as well as the exceptional group G2. For these groups, we demonstrate that all split forms satisfy the mixed Tate property, while exhibiting non-split forms that do not. Finally, we prove that for any affine group scheme G and normal split unipotent subgroup J of G, the motives Mc(BG) and Mc(B(G/J)) are isomorphic.