Mathematical Research Letters

Volume 24 (2017)

Number 6

Epimorphic subgroups of algebraic groups

Pages: 1649 – 1665



Michel Brion (Université Grenoble Alpes, Institut Fourier, Grenoble, France)


In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which generalize a result of Bien and Borel. Moreover, we extend the affinization theorem for algebraic groups to homogeneous spaces.

Received 28 June 2016

Accepted 2 January 2017

Published 29 January 2018