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arXiv · 2407.00726

Local-global principle for groups of type An over semi global fields

V. Suresh
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Abstract

Let F be the function field of a curve over a complete discretely valued field K. Let G be a semisimple simply connected linear algebraic group over F of type An. We give a description of the obstruction to local global principle for principal homogeneous spaces under G over F with respect to discrete valuations of F in terms of R-equivalence classes of G over some suitable over fields. Using this description we prove that this obstruction vanishes under some conditions on the residue field K.

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V. Suresh. 2024-06-30. Local-global principle for groups of type An over semi global fields. https://arxiv.org/abs/2407.00726

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