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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
8
votes
2
answers
779
views
When are generalized Severi-Brauer varieties Grassmannians?
Let $F$ be a field and $A$ be an $F$-central simple algebra of degree $n$. Let $0< k< n$ and let $SB_k(A)$ denote the generalized Severi-Brauer variety: if $E/F$ is a field extension, $SB_k(A)(E)$ con …
5
votes
0
answers
147
views
Motives with compact support, Chow groups and proper pushforward maps
In Motivic cohomology of smooth geometrically cellular varieties (1999), Corollary 3.5, Bruno Kahn proves the following statement. Consider a cellular variety $X$ (i.e. it admits a filtration by close …