$G$-prime and $G$-primary $G$-ideals on $G$-schemes

Details $G$-prime and $G$-primary $G$-ideals on $G$-schemes $G$-prime and $G$-primary $G$-ideals on $G$-schemes

2009-06-08

arxiv.org/abs/0906.1441v3

Mathematics

Commutative Algebra

54pages, modified the introduction, references, (3.9), (3.16), (3.18), (4.2), (6.23), and (6.25). Some other minor errors are

Scientific paper

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$-primary decomposition and the well-definedness of $G$-associated $G$-primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$-regular and $F$-rational properties.

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