Comptes Rendus
no. 9
Algebra
A universal deformation ring which is not a complete intersection ring

Presented by: Jean-Pierre Serre

Jakub Byszewski1
1 Department of Mathematics, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands
Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 565-568.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.09.015

Jakub Byszewski 1

1 Department of Mathematics, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands 
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Jakub Byszewski. A universal deformation ring which is not a complete intersection ring. Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 565-568. doi : 10.1016/j.crma.2006.09.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.015/

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

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

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

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

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