Polynomial functors over finite fields

Pirashvili, Teimuraz

Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 877, 20 p.

MR 1886766 | Zbl 0999.19003 | 1 citation dans Numdam

BibTeX
RIS

@incollection{SB_1999-2000__42__369_0,
     author = {Pirashvili, Teimuraz},
     title = {Polynomial functors over finite fields},
     booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:877},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {276},
     year = {2002},
     zbl = {0999.19003},
     mrnumber = {1886766},
     language = {en},
     url = {http://www.numdam.org/item/SB_1999-2000__42__369_0/}
}

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AU  - Pirashvili, Teimuraz
TI  - Polynomial functors over finite fields
BT  - Séminaire Bourbaki : volume 1999/2000, exposés 865-879
AU  - Collectif
T3  - Astérisque
N1  - talk:877
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PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1999-2000__42__369_0/
UR  - https://zbmath.org/?q=an%3A0999.19003
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Pirashvili, Teimuraz. Polynomial functors over finite fields, dans Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 877, 20 p. http://www.numdam.org/item/SB_1999-2000__42__369_0/

Bibliographie
Cité par

[1] S. Betley. Stable $K$ -theory of finite fields. $K$ -Theory 17 (1999), no. 2, 103-111. | MR 1696427 | Zbl 0929.19002

[2] S. Betley & T. Pirashvili. Stable $K$ -theory as a derived functor. J. Pure Appl. Algebra 96 (1994), no. 3, 245-258. | MR 1303284 | Zbl 0812.19002

[3] M. Bökstedt. On the topological Hochschild homology of $𝐙$ and $𝐙 / p 𝐙$ . Bielefeld (1987).

[4] L. Breen. Extensions du groupe additif. Publ. Ihes 48 (1978), 39-125. | Numdam | MR 516914 | Zbl 0404.14018

[5] E. Cline, B. Parshall, L. Scott & W. Van Der Kallen. Rational and generic cohomology. Invent. Math. 39 (1977), 143-163. | MR 439856 | Zbl 0336.20036

[6] S. Donkin. On Schur algebras and related algebras. I. J. Algebra 104 (1986), 310-328. | MR 866778 | Zbl 0606.20038

[7] S. Donkin. On Schur algebras and related algebras. II. J. Algebra 111 (1987), 354-364. | MR 916172 | Zbl 0634.20019

[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. | MR 1307900 | Zbl 0839.55003

[9] W. Dwyer. Twisted homological stability for general linear groups. Ann. of Math. 111 (1980), 239-251. | MR 569072 | Zbl 0404.18012

[10] S. Eilenberg. & S. Mac Lane. On the groups $H (Π, n)$ . II. Ann. of Math. 60 (1954), 49-139. | Zbl 0055.41704

[11] V. Franjou. Extensions entre puissances extérieures et entre puissances symétriques. J. Algebra 179 (1996), 501-522. | MR 1367860 | Zbl 0841.55012

[12] V. Franjou, J. Lannes & L. Schwartz. Autour de la cohomologie de Mac Lane des corps finis. Invent. Math. 115 (1994), 513-538. | MR 1262942 | Zbl 0798.18009

[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. | MR 1726705 | Zbl 0952.20035

[14] E. Friedlander & A. Suslin. Cohomology of finite group schemes over a field. Invent. Math. 127(1997), 209-270. | MR 1427618 | Zbl 0945.14028

[15] J. A. Green. Polynomial representations of $G l_{n}$ . Lecture Notes in Mathematics 830. Springer-Verlag, (1980). | MR 606556 | Zbl 0451.20037

[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. | MR 1246184 | Zbl 0805.55011

[17] H.-W. Henn, J. Lannes & L. Schwartz. Localizations of unstable $A$ -modules and equivariant mod $p$ cohomology. Math. Ann. 301 (1995), 23-68. | MR 1312569 | Zbl 0869.55016

[18] J. C. Jantzen. Representations of algebraic groups. Pure and Applied Mathematics 131. Academic Press, Inc., Boston, Ma (1987). | MR 899071 | Zbl 0654.20039

[19] M. Jibladze & T. Pirashvili. Cohomology of algebraic theories. J. Algebra 137 (1991), 253-296. | MR 1094244 | Zbl 0724.18005

[20] N. J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. I. Amer. J. Math. 116 (1994), 327-360. | MR 1269607 | Zbl 0813.20049

[21] N. J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. II. $K$ -Theory 8 (1994), 395-428. | MR 1300547 | Zbl 0830.20065

[22] N. J. Kuhn. Generic representations of the finite general linear groups and the Steenrod algebra. III. $K$ -Theory 9 (1995), 273-303. | MR 1344142 | Zbl 0831.20057

[23] N. J. Kuhn. On topologically realizing modules over the Steenrod algebra. Ann. of Math. (2) 141 (1995), 321-347. | MR 1324137 | Zbl 0849.55022

[24] I. G. Macdonald. Symmetric functions and Hall polynomials. Second edition. Oxford University Press (1995). | MR 1354144 | Zbl 0899.05068

[25] S. Martin. Schur algebras and representation theory. Cambridge University Press (1993). | MR 1268640 | Zbl 0802.20011

[26] T. Pirashvili. Polynomial functors. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. Ssr 91 (1988), 55-66. | MR 1029007 | Zbl 0705.18009

[27] T. Pirashvili. Higher additivizations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. Ssr 91 (1988), 44-54. | MR 1029006 | Zbl 0705.18008

[28] T. Pirashvili. New homology and cohomology of rings. (Russian) Soobshch. Akad. Nauk Gruzin. Ssr 133 (1989), no. 3, 477-480. | MR 1033967 | Zbl 0676.16024

[29] T. Pirashvili & F. Waldhausen. Mac Lane homology and topological Hochschild homology. J. Pure Appl. Algebra 82 (1992), no. 1, 81-98. | MR 1181095 | Zbl 0767.55010

[30] L. Piriou & L. Schwartz. Extensions de foncteurs simples. $K$ -Theory 15 (1998), 269-291. | MR 1659961 | Zbl 0918.20036

[31] G. Powell. The Artinian conjecture for $I^{\otimes 2}$ . J. Pure Appl. Algebra 128 (1998), 291-310. | Zbl 0928.18004

[32] N. Roby. Lois polynômes et lois formelles en théorie des modules. Ann. Sci. Éc. Norm. Sup. (3) 80 (1963) 213-348. | Numdam | MR 161887 | Zbl 0117.02302

[33] D. Quillen. On the cohomology and $K$ -theory of the general groups over a finite field, Ann. of Math. 96 (1972), 552-586. | MR 315016 | Zbl 0249.18022

[34] L. Schwartz. Unstable modules over the Steenrod algebra and Sullivan's fixed point set conjecture. University of Chicago Press (1994). | MR 1282727 | Zbl 0871.55001

[35] L. Schwartz. À propos de la conjecture de non-réalisation due à N. Kuhn. Invent. Math. 134 (1998), no. 1, 211-227. | MR 1646599 | Zbl 0919.55007

[36] B. Totaro. Projective resolutions of representations of $G l (n)$ . J. Reine Angew. Math. 482 (1997), 1-13. | MR 1427655 | Zbl 0859.20034