Polynomial functors over finite fields

Teimuraz Pirashvili

Séminaire Bourbaki (1999-2000)

  • Volume: 42, page 369-388
  • ISSN: 0303-1179

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Pirashvili, Teimuraz. "Polynomial functors over finite fields." Séminaire Bourbaki 42 (1999-2000): 369-388. <http://eudml.org/doc/110280>.

@article{Pirashvili1999-2000,
author = {Pirashvili, Teimuraz},
journal = {Séminaire Bourbaki},
keywords = {polynomial functors; Steenrod algebra; Schur algebra; polynomial representations; general linear group; stable -theory},
language = {eng},
pages = {369-388},
publisher = {Société Mathématique de France},
title = {Polynomial functors over finite fields},
url = {http://eudml.org/doc/110280},
volume = {42},
year = {1999-2000},
}

TY - JOUR
AU - Pirashvili, Teimuraz
TI - Polynomial functors over finite fields
JO - Séminaire Bourbaki
PY - 1999-2000
PB - Société Mathématique de France
VL - 42
SP - 369
EP - 388
LA - eng
KW - polynomial functors; Steenrod algebra; Schur algebra; polynomial representations; general linear group; stable -theory
UR - http://eudml.org/doc/110280
ER -

References

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  1. [1] S. Betley. Stable K-theory of finite fields. K-Theory17 (1999), no. 2, 103-111. Zbl0929.19002MR1696427
  2. [2] S. Betley & T. Pirashvili. Stable K-theory as a derived functor. J. Pure Appl. Algebra96 (1994), no. 3, 245-258. Zbl0812.19002MR1303284
  3. [3] M. Bökstedt. On the topological Hochschild homology of Z and Z/pZ. Bielefeld (1987). 
  4. [4] L. Breen. Extensions du groupe additif. Publ. Ihes48 (1978), 39-125. Zbl0404.14018MR516914
  5. [5] E. Cline, B. Parshall, L. Scott & W. Van Der Kallen. Rational and generic cohomology. Invent. Math.39 (1977), 143-163. Zbl0336.20036MR439856
  6. [6] S. Donkin. On Schur algebras and related algebras. I. J. Algebra104 (1986), 310-328. Zbl0606.20038MR866778
  7. [7] S. Donkin. On Schur algebras and related algebras. II. J. Algebra111 (1987), 354-364. Zbl0634.20019MR916172
  8. [8] B. Dundas & R. Mccarthy. Stable K-theory and topological Hochschild homology, Ann. of Math.140 (1994), 685-701; erratum: Ann. of Math.142 (1995), 425-426. Zbl0839.55003MR1307900
  9. [9] W. Dwyer. Twisted homological stability for general linear groups. Ann. of Math.111 (1980), 239-251. Zbl0404.18012MR569072
  10. [10] S. Eilenberg. & S. Mac Lane. On the groups H(π,n). II. Ann. of Math.60 (1954), 49-139. Zbl0055.41704
  11. [11] V. Franjou. Extensions entre puissances extérieures et entre puissances symétriques. J. Algebra179 (1996), 501-522. Zbl0841.55012MR1367860
  12. [12] V. Franjou, J. Lannes & L. Schwartz. Autour de la cohomologie de Mac Lane des corps finis. Invent. Math.115 (1994), 513-538. Zbl0798.18009MR1262942
  13. [13] V. Franjou, E. Friedlander, A. Scorichenko & A. Suslin. General linear and functor cohomology over finite fields. Ann. of Math. (2) 150 (1999), 663-728. Zbl0952.20035MR1726705
  14. [14] E. Friedlander & A. Suslin. Cohomology of finite group schemes over a field. Invent. Math.127(1997), 209-270. Zbl0945.14028MR1427618
  15. [15] J.A. Green. Polynomial representations of Gln. Lecture Notes in Mathematics830. Springer-Verlag, (1980). Zbl0451.20037MR606556
  16. [16] H.-W. Henn, J. Lannes & L. Schwartz. The categories of unstable modules and unstable algebras over the Steenrod algebra modulo nilpotent objects. Amer. J. Math.115 (1993), 1053-1106. Zbl0805.55011MR1246184
  17. [17] H.-W. Henn, J. Lannes & L. Schwartz. Localizations of unstable A-modules and equivariant mod p cohomology. Math. Ann.301 (1995), 23-68. Zbl0869.55016MR1312569
  18. [18] J.C. Jantzen. Representations of algebraic groups. Pure and Applied Mathematics131. Academic Press, Inc., Boston, Ma (1987). Zbl0654.20039MR899071
  19. [19] M. Jibladze & T. Pirashvili. Cohomology of algebraic theories. J. Algebra137 (1991), 253-296. Zbl0724.18005MR1094244
  20. [20] N.J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. I. Amer. J. Math.116 (1994), 327-360. Zbl0813.20049MR1269607
  21. [21] N.J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. II. K-Theory8 (1994), 395-428. Zbl0830.20065MR1300547
  22. [22] N.J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. III. K-Theory9 (1995), 273-303. Zbl0831.20057MR1344142
  23. [23] N.J. Kuhn. On topologically realizing modules over the Steenrod algebra. Ann. of Math. (2) 141 (1995), 321-347. Zbl0849.55022MR1324137
  24. [24] I.G. Macdonald. Symmetric functions and Hall polynomials. Second edition. Oxford University Press (1995). Zbl0899.05068MR1354144
  25. [25] S. Martin. Schur algebras and representation theory. Cambridge University Press (1993). Zbl0802.20011MR1268640
  26. [26] T. Pirashvili. Polynomial functors. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. Ssr91 (1988), 55-66. Zbl0705.18009MR1029007
  27. [27] T. Pirashvili. Higher additivizations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. Ssr91 (1988), 44-54. Zbl0705.18008MR1029006
  28. [28] T. Pirashvili. New homology and cohomology of rings. (Russian) Soobshch. Akad. Nauk Gruzin. Ssr133 (1989), no. 3, 477-480. Zbl0676.16024MR1033967
  29. [29] T. Pirashvili & F. Waldhausen. Mac Lane homology and topological Hochschild homology. J. Pure Appl. Algebra82 (1992), no. 1, 81-98. Zbl0767.55010MR1181095
  30. [30] L. Piriou & L. Schwartz. Extensions de foncteurs simples. K-Theory15 (1998), 269-291. Zbl0918.20036MR1659961
  31. [31] G. Powell. The Artinian conjecture for I⊗2. J. Pure Appl. Algebra128 (1998), 291-310. Zbl0928.18004
  32. [32] N. Roby. Lois polynômes et lois formelles en théorie des modules. Ann. Sci. Éc. Norm. Sup. (3) 80 (1963) 213-348. Zbl0117.02302MR161887
  33. [33] D. Quillen. On the cohomology and K-theory of the general groups over a finite field, Ann. of Math.96 (1972), 552-586. Zbl0249.18022MR315016
  34. [34] L. Schwartz. Unstable modules over the Steenrod algebra and Sullivan's fixed point set conjecture. University of Chicago Press (1994). Zbl0871.55001MR1282727
  35. [35] L. Schwartz. À propos de la conjecture de non-réalisation due à N. Kuhn. Invent. Math.134 (1998), no. 1, 211-227. Zbl0919.55007MR1646599
  36. [36] B. Totaro. Projective resolutions of representations of Gl(n). J. Reine Angew. Math.482 (1997), 1-13. Zbl0859.20034MR1427655

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