Hostname: page-component-7bb8b95d7b-495rp Total loading time: 0 Render date: 2024-09-06T21:35:59.416Z Has data issue: false hasContentIssue false
  • English
  • Français

Completions of rings of invariants and their divisor class groups

Published online by Cambridge University Press:  22 January 2016

Phillip Griffith
Phillip Griffith*
Affiliation:
Illinois University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k be a field and let A = be a normal graded subring of the full ring of polynomials R = k[X1, · · ·, Xn] (where R always is graded via total degree and A0 = k). R. Fossum and the author [F-G] observed that the completion  at the irrelevant maximal ideal of A is isomorphic to the subring of the formal power series ring R̂ = k[[X1, · ·., Xn]] and, moreover, that  is a ring of invariants of an algebraic group whenever A is.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 72 , December 1978 , pp. 71 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[B] Bertin, M.-J., Anneaux d’invariants d’anneaux de polynômes, en caractéristique p, C. R. Acad. Sc, Paris, t. 264, série A (1967), 653’656.Google Scholar
[D] Danilov, V. I., On a conjecture of Samuel,—Math. USSR-S610, 127’137 (1970) (Mat. sb. 81 (123), 132’144 (1970)).Google Scholar
[D-G] Demazure, M. and Gabriel, P., Groupes Algébriques, North-Holland Publishing Co., Amsterdam, (1970).Google Scholar
[F] Fossum, R., The Divisor Class Group of a Krull Domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 74, Berlin-Heidelberg-New York, Springer, (1973).CrossRefGoogle Scholar
[F-G] Fossum, R. and Griffith, P., Complete local factorial rings which are not CohenMacaulay in characteristic p , Ann. Scient. Ec. Norm. Sup., 4eserie, t. 8 (1975), 189’200.Google Scholar
[EGA] Grothendieck, A. and Dieudonne, J., Elements de Geometric algébrique I.H.E.S. Pubi. Math., Vol. I, no. 4, 1960.Google Scholar
[M] Magid, A., Finite generation of class groups of rings of invariants, Proc. A.M.S. 60 (1976), 45’48.Google Scholar