Local-global principle for classical groups over function fields of pp-adic curves

  • Raman Parimala

    Emory University, Atlanta, USA
  • Venapally Suresh

    Emory University, Atlanta, USA
Local-global principle for classical groups over function fields of $p$-adic curves cover
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Abstract

Let KK be a local field with residue field κ\kappa and FF the function field of a curve over KK. Let GG be a connected linear algebraic group over FF of classical type. Suppose char(κ)\operatorname{char}(\kappa) is a good prime for GG. Then we prove that projective homogeneous spaces under GG over FF satisfy a local-global principle for rational points with respect to discrete valuations of FF. If GG is a semisimple simply connected group over FF, then we also prove that principal homogeneous spaces under GG over FF satisfy a local-global principle for rational points with respect to discrete valuations of FF.

Cite this article

Raman Parimala, Venapally Suresh, Local-global principle for classical groups over function fields of pp-adic curves. Comment. Math. Helv. 97 (2022), no. 2, pp. 255–304

DOI 10.4171/CMH/531