no. 9
Algebra
A universal deformation ring which is not a complete intersection ring
[Un anneau de déformation qui n'est pas d'intersection complète]

Présenté par : Jean-Pierre Serre

Byszewski, Jakub1
1 Department of Mathematics, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands
Comptes Rendus. Mathématique, Tome 343 (2006) no. 9, pp. 565-568.

Bleher et Chinburg ont récemment utilisé la théorie des réprésentation modulaires pour construire une représentation d'un groupe fini ayant un anneau de déformations universel qui n'est pas d'intersection complète. On redémontre ce résultat en n'utilisant que la théorie cohomologique des obstructions.

Bleher and Chinburg recently used modular representation theory to produce an example of a linear representation of a finite group whose universal deformation ring is not a complete intersection ring. We prove this by using only elementary cohomological obstruction calculus.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.015
Byszewski, Jakub 1

1 Department of Mathematics, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands 
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Byszewski, Jakub. A universal deformation ring which is not a complete intersection ring. Comptes Rendus. Mathématique, Tome 343 (2006) no. 9, pp. 565-568. doi : 10.1016/j.crma.2006.09.015. http://www.numdam.org/articles/10.1016/j.crma.2006.09.015/

[1] Bleher, F.M.; Chinburg, T. Universal deformation rings need not be complete intersections, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 229-232

[2] Mazur, B. An introduction to the deformation theory of Galois representations (Cornell, G.; Silverman, J.H.; Stevens, G., eds.), Modular Forms and Fermat's Last Theorem, Springer-Verlag, 1997, pp. 243-312

[3] Schlessinger, M. Functors of Artin rings, Trans. Amer. Math. Soc., Volume 130 (1968), pp. 208-222

[4] Serre, J.-P. Local Fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, 1979

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