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August 2022 Homomorphisms of Algebraic Groups: Representability and Rigidity
Michel Brion
Michigan Math. J. 72: 51-76 (August 2022). DOI: 10.1307/mmj/20217214

Abstract

Given two algebraic groups G, H over a field k, we investigate the representability of the functor of morphisms (of schemes) Hom(G,H) and the subfunctor of homomorphisms (of algebraic groups) Homgp(G,H). We show that Hom(G,H) is represented by a group scheme, locally of finite type, if the k-vector space O(G) is finite-dimensional; the converse holds if H is not étale. When G is linearly reductive and H is smooth, we show that Homgp(G,H) is represented by a smooth scheme M; moreover, every orbit of H acting by conjugation on M is open.

Citation

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Michel Brion. "Homomorphisms of Algebraic Groups: Representability and Rigidity." Michigan Math. J. 72 51 - 76, August 2022. https://doi.org/10.1307/mmj/20217214

Information

Received: 21 May 2021; Revised: 5 August 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217214

Subjects:
Primary: 14L15
Secondary: 14D20 , 14K05 , 14L30 , 20G15

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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