Anti-affine algebraic groups

Details Anti-affine algebraic groups Anti-affine algebraic groups

2007-10-27

arxiv.org/abs/0710.5211v3

Mathematics

Algebraic Geometry

Prior work of Carlos Sancho de Salas acknowledged, additional minor changes,

Scientific paper

We say that an algebraic group $G$ over a field is anti-affine if every
regular function on $G$ is constant. We obtain a classification of these
groups, with applications to the structure of algebraic groups in positive
characteristics, and to the construction of many counterexamples to Hilbert's
fourteenth problem.

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