Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

On support varieties for modules over complete intersections

Author(s): Petter Andreas Bergh
Journal: Proc. Amer. Math. Soc. 135 (2007), 3795-3803.
MSC (2000): Primary 13C14, 13C40, 13D07, 14M10; Secondary 20J06
Posted: September 7, 2007
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: Let $ (A, \mathfrak{m}, k)$ be a complete intersection of codimension $ c$, and let $ \tilde{k}$ be the algebraic closure of $ k$. We show that every homogeneous algebraic subset of $ \tilde{k}^c$ is the cohomological support variety of an $ A$-module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay $ A$-module is connected.

References:

[AuB]
M. Auslander, R.-O. Buchweitz, The homological theory of maximal Cohen-Macaulay approximations, Mém. Soc. Math. France 38 (1989), 5-37. MR 1044344 (91h:13010)

[Avr]
L. Avramov, Modules of finite virtual projective dimension, Invent. Math. 96 (1989), 71-101. MR 981738 (90g:13027)

[AvB]
L. Avramov, R.-O. Buchweitz, Support varieties and cohomology over complete intersections, Invent. Math. 142 (2000), 285-318. MR 1794064 (2001j:13017)

[AGP]
L. Avramov, V. Gasharov, I. Peeva, Complete intersection dimension, Publ. Math. I.H.E.S. 86 (1997), 67-114. MR 1608565 (99c:13033)

[ArY]
T. Araya, Y. Yoshino, Remarks on a depth formula, a grade inequality and a conjecture of Auslander, Comm. Algebra 26 (1998), 3793-3806. MR 1647079 (99h:13010)

[Ber]
P.A. Bergh, Modules with reducible complexity, J. Algebra 310 (2007), no. 1, 132-147.

[Car]
J. Carlson, The variety of an indecomposable module is connected, Invent. Math. 77 (1984), 291-299. MR 752822 (86b:20009)

[EHSST]
K. Erdmann, M. Holloway, N. Snashall, Ø. Solberg, R. Taillefer, Support varieties for selfinjective algebras, $ K$-theory 33 (2004), 67-87. MR 2199789

[Mar]
A. Martsinkovsky, Cohen-Macaulay modules and approximations, in Trends in Mathematics: Infinite Length Modules, H. Krause and C. Ringel (eds.), Birkhäuser Verlag (2000), 167-192. MR 1789215 (2001i:13011)

[Mat]
H. Matsumura, Commutative ring theory, Cambridge University Press, 2000. MR 879273 (88h:13001)

[SnS]
N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (2004), 705-732. MR 2044054 (2005a:16014)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13C14, 13C40, 13D07, 14M10, 20J06

Retrieve articles in all Journals with MSC (2000): 13C14, 13C40, 13D07, 14M10, 20J06

Additional Information:

Petter Andreas Bergh
Affiliation: Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
Email: bergh@math.ntnu.no

DOI: 10.1090/S0002-9939-07-09009-0
PII: S 0002-9939(07)09009-0
Keywords: Complete intersections, support varieties.
Received by editor(s): June 13, 2006
Received by editor(s) in revised form: September 26, 2006
Posted: September 7, 2007
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google