# Local-global principle for classical groups over function fields of $p$-adic curves

### Raman Parimala

Emory University, Atlanta, USA### Venapally Suresh

Emory University, Atlanta, USA

## Abstract

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

## Cite this article

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

DOI 10.4171/CMH/531