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arXiv · 2410.15598

Rost injectivity for classical groups over function fields of curves over local fields

R. Parimala·V. Suresh
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Abstract

Let F be a complete discretely valued field with residue field a global field or a local field with no real orderings. Let G be an absolutely simple simply connected group of outer type A_n. If 2 and the index of the underlying algebra of G are coprime to the characteristic of the residue field of F, then we prove that the Rost invariant map from the first Galois cohomology set of G to the degree three Galois cohomology group is injective. Let L be the function field of a curve over a local field K and G an absolutely simple simply connected linear algebraic group over L of classical type. Suppose that the characteristic of the residue field of K is a good prime for G. As a consequence of our result and some known results we conclude that the Rost invariant of G is injective.

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BibTeXRIS

R. Parimala, V. Suresh. 2024-10-21. Rost injectivity for classical groups over function fields of curves over local fields. https://arxiv.org/abs/2410.15598

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