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Strictly contracting elements in the center of a Levi subgroup

Let $G$ be a connected reductive group of an arbitrary field $k$, $P$ a parabolic $k$-subgroup, and $U = \mathscr{R}_u(P)$ the unipotent radical of $P$ (so $U$ is what is unfortunately traditionally d …
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equivalence of quadratic forms over finitely generated fields

By "Hasse invariant" I suppose you mean a 2-torsion class in the Brauer group (which can be further analyzed via local Brauer groups, but that step is specific to global fields). And by "signature" yo …
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