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Support varieties
for infinitesimal group schemes


Authors: Andrei Suslin, Eric M. Friedlander and Christopher P. Bendel
Journal: J. Amer. Math. Soc. 10 (1997), 729-759
MSC (1991): Primary 14L15, 20C20, 20G10; Secondary 17B50
DOI: https://doi.org/10.1090/S0894-0347-97-00239-7
MathSciNet review: 1443547
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  • [A-E] J. Alperin and L. Evens, Representations, resolutions, and Quillen's dimension theorem, J.P.A.A. 22 (1981), 1-9. MR 82j:20020
  • [A-J] H Andersen and J. Jantzen, Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1985), 487-525. MR 86g:20057
  • [A-S] G. Avrunin and L. Scott, Quillen stratification for modules, Inventiones Math. 66 (1982), 277-286. MR 83h:20048
  • [B] H.Bass, Algebraic K-theory (W.A.Benjamin, Inc, ed.), 1968. MR 40:2736
  • [C1] J. Carlson, The varieties and the cohomology ring of a module, J. Algebra 85 (1983), 104-143. MR 85a:20004
  • [C2] J. Carlson, The variety of an indecomposable module is connected, Inventiones Math. 77 (1984), 291-299. MR 86b:20009
  • [CPS] E. Cline, B. Parshall, and L. Scott, On injective modules for infinitesimal algebraic groups, I, J. Lond Math. Soc. 31 (1985), 277-291. MR 87c:20077
  • [CPSvdK] E. Cline, B. Parhall, L. Scott, and W. van der Kallen, Rational and generic cohomology, Inventiones Math. 39 (1977), 143-163. MR 55:12737
  • [D-G] M. Demazure and P. Gabriel, Groupes algébriques I (Masson/North-Holland, ed.), 1970. MR 46:1800
  • [D] A. Dold, Über die Steenrodschen Kohomologieoperationen, Ann. Math 73 (1961), 258-294. MR 23:A646
  • [E] L. Evens, The Cohomology of Groups (Oxford Univ. Press, ed.), 1991. MR 93i:20059
  • [FP1] E. Friedlander and B. Parshall, On the cohomology of algebraic groups and related finite groups, Inventiones Math. 74 (1983), 85-117. MR 85d:20035
  • [FP2] E. Friedlander and B. Parshall, Cohomology of Lie algebras and algebraic groups, Amer. J. Math. 108 (1986), 235-253. MR 87c:20080
  • [FP3] E. Friedlander and B. Parshall, Geometry of p-Unipotent Lie algebras, J. Algebra 109 (1987), 25-45. MR 89a:17017
  • [FP4] E. Friedlander and B. Parshall, Support varieties for restricted Lie algebras, Inventiones Math. 86 (1986), 553-562. MR 88f:17018
  • [F-S] E. Friedlander and A. Suslin, Cohomology of finite group schemes over a field, Inventiones Math. 127 (1997), 209-270. CMP 97:06
  • [J1] J. Jantzen, Kohomologie von $p$-Lie Algebren und nilpotente Elemente, Abh. Math. Sem. Univ. Hamburg 56 (1986), 191-219. MR 88e:17019
  • [J] J. Jantzen, Representations of Algebraic Groups (Academic Press, ed.), 1987. MR 89c:20001
  • [K] W. van der Kallen, Infinitesimally central extensions of $Spin_{7}$ in characteristic 2, J.P.A.A. 14 (1979), 39-49. MR 81h:20050
  • [M] J. P. May, A general algebraic approach to Steenrod operations., The Steenrod Algebra and its Applications (Springer Verlag, LNM 168, ed.), 1970, pp. 153-231. MR 43:6915
  • [Mi] J. S. Milne, Etale Cohomology (Princeton Unversity Press, ed.), 1980. MR 81j:14002
  • [P] S. Priddy, Mod-$p$ right derived functor algebras of the symmetric algebra functor, J.P.A.A. 3 (1973), 337-356. MR 49:7338
  • [Q] D. Quillen, The spectrum of an equivariant cohomology ring: I, II, Ann. Math. 94 (1971), 549-572, 573-602. MR 45:7743
  • [Q-V] D. Quillen and B. Venkov, Cohomology of finite groups and elementary abelian subgroups, Topology 11 (1972), 317-318. MR 45:3576
  • [S] J.-P. Serre, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413-420. MR 31:4853
  • [S-F-B] A. Suslin, E. Friedlander, and C. Bendel, Infinitesimal 1-parameter subgroups and cohomology, Journal of the American Mathematical Society (this volume).
  • [SGA1] A.Grothendieck, Revêtements Étales et Groupe Fondamental (Springer Verlag, LNM 224, ed.), 1971. MR 50:7129

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Additional Information

Andrei Suslin
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: suslin@math.nwu.edu

Eric M. Friedlander
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: eric@math.nwu.edu

Christopher P. Bendel
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: bendelmath.nwu.edu

DOI: https://doi.org/10.1090/S0894-0347-97-00239-7
Keywords: Infinitesimal group schemes, support varieties, 1-parameter subgroups.
Received by editor(s): October 25, 1996
Received by editor(s) in revised form: March 20, 1997
Additional Notes: The first author was partially supported by I.S.F. grant 0100 and N.S.F. grant DMS - 9510242.
The second author was partially supported by the N.S.F. and the Humboldt Foundation.
Article copyright: © Copyright 1997 American Mathematical Society

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