Local-global principle for classical groups over function fields of -adic curves
Raman Parimala
Emory University, Atlanta, USAVenapally Suresh
Emory University, Atlanta, USA
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Abstract
Let be a local field with residue field and the function field of a curve over . Let be a connected linear algebraic group over of classical type. Suppose is a good prime for . Then we prove that projective homogeneous spaces under over satisfy a local-global principle for rational points with respect to discrete valuations of . If is a semisimple simply connected group over , then we also prove that principal homogeneous spaces under over satisfy a local-global principle for rational points with respect to discrete valuations of .
Cite this article
Raman Parimala, Venapally Suresh, Local-global principle for classical groups over function fields of -adic curves. Comment. Math. Helv. 97 (2022), no. 2, pp. 255–304
DOI 10.4171/CMH/531