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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Submersive and unipotent group quotients among schemes of a countable type over a field $ k$

Author: Paul Cherenack
Journal: Trans. Amer. Math. Soc. 211 (1975), 101-112
MSC: Primary 14M15; Secondary 20G15
MathSciNet review: 0376700
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Abstract: An algebraic group G is called submersive if every quotient in affine schemes $ {c^G}:{\text{Spec}}\;A \to {\text{Spec}}\;{A^G}$ which is surjective is also submersive. We prove that every unipotent group is submersive. Suppose G is submersive. We show that if $ {c^G}({\text{Spec}}\;A)$ is open in $ {\text{Spec}}\;{A^G}$ or if some restrictions on the action of G on A are made, $ {c^G}$ is a topological quotient. A criterion for semisimplicity of points is extended to the case where G is unipotent. Finally, applications of the theory are provided.

References [Enhancements On Off] (What's this?)

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Keywords: Submersive group, unipotent group, scheme of a countable type over k, affine scheme, algebraic group quotient, reductive group, relative coequalizer, semistable point, Hilbert's fourteenth problem, Nagata's counterexample, linear systems, Chevalley's theorem, constructible set
Article copyright: © Copyright 1975 American Mathematical Society