### Abstract

Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → B^{G} be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)^{K⊗G} is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗ A → (S ⊗ B)^{S⊗G} is an isomorphism for any R-algebra S.

Original language | English |
---|---|

Pages (from-to) | 165-171 |

Number of pages | 7 |

Journal | Nagoya Mathematical Journal |

Volume | 186 |

Publication status | Published - 2007 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Base change of invariant subrings.** / Hashimoto, Mitsuyasu.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 186, pp. 165-171.

}

TY - JOUR

T1 - Base change of invariant subrings

AU - Hashimoto, Mitsuyasu

PY - 2007

Y1 - 2007

N2 - Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗ A → (S ⊗ B)S⊗G is an isomorphism for any R-algebra S.

AB - Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗ B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗ A → (S ⊗ B)S⊗G is an isomorphism for any R-algebra S.

UR - http://www.scopus.com/inward/record.url?scp=38349126998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349126998&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38349126998

VL - 186

SP - 165

EP - 171

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -