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- W4301030735 abstract "Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $pi: V to V//G$ denote the quotient map. Arithmetic invariant theory studies the map $pi$ on the level of $k$-rational points. In this article, which is a continuation of the results of our earlier paper Arithmetic invariant theory, we provide necessary and sufficient conditions for a rational element of $V//G$ to lie in the image of $pi$, assuming that generic stabilizers are abelian. We illustrate the various scenarios that can occur with some recent examples of arithmetic interest." @default.
- W4301030735 created "2022-10-04" @default.
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- W4301030735 date "2013-10-29" @default.
- W4301030735 modified "2023-09-27" @default.
- W4301030735 title "Arithmetic invariant theory II" @default.
- W4301030735 doi "https://doi.org/10.48550/arxiv.1310.7689" @default.
- W4301030735 hasPublicationYear "2013" @default.
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