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A universal deformation ring which is not a complete intersection ring. (English) Zbl 1134.20302

Summary: F. M. Bleher and T. Chinburg [C. R., Math., Acad. Sci. Paris 342, No. 4, 229-232 (2006; Zbl 1087.11065)] 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.

MSC:

20C15 Ordinary representations and characters
19A22 Frobenius induction, Burnside and representation rings
11F80 Galois representations

Citations:

Zbl 1087.11065
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Full Text: DOI

References:

[1] Bleher, F. M.; Chinburg, T., Universal deformation rings need not be complete intersections, C. R. Acad. Sci. Paris, Ser. I, 342, 229-232 (2006) · Zbl 1087.11065
[2] Mazur, B., An introduction to the deformation theory of Galois representations, (Cornell, G.; Silverman, J. H.; Stevens, G., Modular Forms and Fermat’s Last Theorem (1997), Springer-Verlag), 243-312 · Zbl 0901.11015
[3] Schlessinger, M., Functors of Artin rings, Trans. Amer. Math. Soc., 130, 208-222 (1968) · Zbl 0167.49503
[4] Serre, J.-P., Local Fields, Graduate Texts in Mathematics, vol. 67 (1979), Springer-Verlag
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