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)
     

Projectivity of modules for infinitesimal unipotent group schemes

Author(s): Christopher P. Bendel
Journal: Proc. Amer. Math. Soc. 129 (2001), 671-676.
MSC (2000): Primary 14L15, 20G05; Secondary 17B50
Posted: September 20, 2000
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this paper, it is shown that the projectivity of a rational module for an infinitesimal unipotent group scheme over an algebraically closed field of positive characteristic can be detected on a family of closed subgroups.


References:

[Ben]
D.J. Benson, Representations and cohomology, Volumes I and II, Cambridge University Press, 1991. MR 92m:20005; MR 93g:20099

[BCR1]
D.J. Benson, J.F. Carlson, and J. Rickard, Complexity and varieties for infinitely generated modules, Math. Proc. Camb. Phil. Soc. 118 (1995), 223-243. MR 96j:20006

[BCR2]
D.J. Benson, J.F. Carlson, and J. Rickard, Complexity and varieties for infinitely generated modules, II, Math. Proc. Camb. Phil. Soc. 120 (1996), 597-615. MR 97f:20008

[Ca]
J.F. Carlson, The varieties and cohomology ring of a module, J. Algebra 85 (1983), 104-143. MR 85a:20004

[Ch]
L. Chouinard, Projectivity and relative projectivity over group rings, J. Pure & Applied Algebra 7 (1976), 287-302. MR 53:5769

[CPS]
E. Cline, B. Parshall, and L. Scott, On injective modules for infinitesimal algebraic groups, I, J. London Math. Soc. (2) 31 (1985), 277-291. MR 87c:20077

[CPSvdK]
E. Cline, B. Parshall, L. Scott, and W. van der Kallen, Rational and generic cohomology, Inventiones Math. 39 (1977), 143-163. MR 55:12737

[Dade]
E.C. Dade, Endo-permutation modules over $p$-groups, II, Annals of Math. 108 (1978), 317-346. MR 80a:13008b

[FW]
C.G. Faith, E.A. Walker, Direct-sum representations of injective modules, J. Algebra 5 (1967), 203-221. MR 34:7575

[Jan]
J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987. MR 89c:20001

[Rim]
D.S. Rim, Modules over finite groups, Annals of Math. 69 (1959), 700-712. MR 21:3474

[Se]
J.-P. Serre, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413-420. MR 31:4853

[SFB1]
A. Suslin, E.M. Friedlander, C.P. Bendel, Infinitesimal 1-parameter subgroups and cohomology, Jour. Amer. Math. Soc. 10 (1997), 693-728. MR 98h:14055b

[SFB2]
A. Suslin, E.M. Friedlander, C.P. Bendel, Support varieties for infinitesimal group schemes, Jour. Amer. Math. Soc. 10 (1997), 729-759. MR 98h:14055c

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14L15, 20G05, 17B50

Retrieve articles in all Journals with MSC (2000): 14L15, 20G05, 17B50


Additional Information:

Christopher P. Bendel
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication: Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout, Menomonie, Wisconsin 54751
Email: bendelc@uwstout.edu

DOI: 10.1090/S0002-9939-00-04951-0
PII: S 0002-9939(00)04951-0
Received by editor(s): January 27, 1998
Received by editor(s) in revised form: March 24, 1998 and May 19, 1999
Posted: September 20, 2000
Communicated by: Lance W. Small
Copyright of article: Copyright 2000, American Mathematical Society


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