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 → 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.
| 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.
In: Nagoya Mathematical Journal, Vol. 186, 2007, p. 165-171.Research output: Contribution to journal › Article
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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 -