JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 1, Pages 85 - 94
(January 2019) http://dx.doi.org/10.17654/NT041010085 |
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INVARIANT PRINCIPAL FRACTIONAL MODULES OF AFFINE INTEGRAL SCHEMES UNDER ALGEBRAIC GROUP ACTIONS
Haruhisa Nakajima
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Abstract: Let G be an affine connected algebraic group acting regularly on an affine integral scheme X = Spec(R) not necessarily of finite type, over an algebraically closed field K with a quotient field Consider a G-rational twisted RG-module M having a non-trivial principal R-submodule Rz of We will show: if Rz is G‑invariant, then so is Kz. Furthermore we study on the G-rationality of Kz in several cases. |
Keywords and phrases: algebraic group, semi-invariant, Krull domain.
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