no. 2
Obstructions for deformations of complexes
[Obstructions pour déformations de complexes]
Bleher, Frauke M.1 ; Chinburg, Ted2
1 University of Iowa Department of Mathematics Iowa City, IA 52242-1419 (U.S.A.)
2 University of Pennsylvania Department of Mathematics Philadelphia, PA 19104-6395 (U.S.A.)
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 613-654.

Nous développons deux approches de la théorie de l’obstruction des déformations de classes d’isomorphisme dans la catégorie dérivée des complexes de A[[G]]-modules lorsque G est un groupe profini et A un anneau local, noethérien complet, de caractéristique positive résiduelle.

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group G over a complete local Noetherian ring A of positive residue characteristic.

DOI : 10.5802/aif.2771
Classification : 11F80, 20E18, 18E30, 18G40
Keywords: Versal and universal deformations, derived categories, obstructions, spectral sequences
Mot clés : déformations verselles et universelles, catégories dérivées, obstructions, suites spectrales
Bleher, Frauke M. 1 ; Chinburg, Ted 2

1 University of Iowa Department of Mathematics Iowa City, IA 52242-1419 (U.S.A.)
2 University of Pennsylvania Department of Mathematics Philadelphia, PA 19104-6395 (U.S.A.) 
@article{AIF_2013__63_2_613_0,
     author = {Bleher, Frauke M. and Chinburg, Ted},
     title = {Obstructions for deformations of complexes},
     journal = {Annales de l'Institut Fourier},
     pages = {613--654},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {63},
     number = {2},
     year = {2013},
     doi = {10.5802/aif.2771},
     zbl = {06193042},
     mrnumber = {3112843},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2771/}
}
TY  - JOUR
AU  - Bleher, Frauke M.
AU  - Chinburg, Ted
TI  - Obstructions for deformations of complexes
JO  - Annales de l'Institut Fourier
PY  - 2013
SP  - 613
EP  - 654
VL  - 63
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2771/
DO  - 10.5802/aif.2771
LA  - en
ID  - AIF_2013__63_2_613_0
ER  - 
%0 Journal Article
%A Bleher, Frauke M.
%A Chinburg, Ted
%T Obstructions for deformations of complexes
%J Annales de l'Institut Fourier
%D 2013
%P 613-654
%V 63
%N 2
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.2771/
%R 10.5802/aif.2771
%G en
%F AIF_2013__63_2_613_0
Bleher, Frauke M.; Chinburg, Ted. Obstructions for deformations of complexes. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 613-654. doi : 10.5802/aif.2771. http://www.numdam.org/articles/10.5802/aif.2771/

[1] Bleher, Frauke M.; Chinburg, Ted Deformations and derived categories, Ann. Institut Fourier (Grenoble), Volume 55 (2005), pp. 2285-2359 | DOI | Numdam | MR | Zbl

[2] Bleher, Frauke M.; Chinburg, Ted Finiteness Theorems for Deformations of Complexes., Ann. Institut Fourier (Grenoble), Volume 63 (2013), pp. 573-612 | DOI

[3] Brumer, Armand Pseudocompact algebras, profinite groups and class formations, J. Algebra, Volume 4 (1966), pp. 442-470 | DOI | MR | Zbl

[4] Gabriel, Pierre Des catégories abéliennes, Bull. Soc. Math. France, Volume 90 (1962), pp. 323-448 | Numdam | MR | Zbl

[5] Gabriel, Pierre Étude infinitésimale des schémas en groupes, A. Grothendieck, SGA 3 (with M. Demazure), Schémas en groupes I, II, III (Lecture Notes in Math. 151), Springer-Verlag, Heidelberg, 1970, pp. 476- 562 | Zbl

[6] Grothendieck, A.; Dieudonné, J. Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I, II, Inst. Hautes Études Sci. Publ. Math. (1961 and 1963) no. 11 and 17, pp. 91 and 167 | Numdam | MR | Zbl

[7] Illusie, Luc Complexe cotangent et déformations. I, II, Lecture Notes in Mathematics, Vol. 239 and 283, Springer-Verlag, Berlin, 1971 and 1972 | MR | Zbl

[8] Mazur, B. Deforming Galois representations, Galois groups over Q (Berkeley, CA, 1987) (Math. Sci. Res. Inst. Publ.), Volume 16, Springer Verlag, Berlin-Heidelberg-New York, 1989, pp. 385-437 | MR | Zbl

[9] Mazur, B. Deformation theory of Galois representations, Modular Forms and Fermat’s Last Theorem (Boston, MA, 1995), Springer Verlag, Berlin-Heidelberg-New York, 1997, pp. 243-311 | MR

[10] Schlessinger, Michael Functors of Artin rings, Trans. Amer. Math. Soc., Volume 130 (1968), pp. 208-222 | DOI | MR | Zbl

[11] Verdier, J.-L. Catégories derivées, P. Deligne, SGA 4.5, Cohomologie étale (Lecture Notes in Math. 569), Springer Verlag, Heidelberg, 1970, pp. 262-311

Cité par Sources :