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Local-global principle for groups of type An over semi global fields (2407.00726v1)
Published 30 Jun 2024 in math.AG and math.NT
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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