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Reduction Theory for a Rational Function Field by Prasad, Amritanshu is a scholarly article available to read on EtoBox.

What is Reduction Theory for a Rational Function Field about?

Let $G$ be a split reductive group over a finite field $\Fq$. Let $F=\Fq(t)$ and let $\A$ denote the ad\`eles of $F$. We show that every double coset in $G(F)\bsl G(\A)/ K$ has a representative in a maximal split torus of $G$. Here $K$ is the set of integral ad\`elic points of $G$. When $G$ ranges over general linear groups this is equivalent to the assertion that any algebraic vector bundle over the projective line is isomorphic to a direct sum of line bundles.

Author

Prasad, Amritanshu

Published

2003

Language

EN