Obstructions for deformations of complexes

Frauke M. Bleher[1]; Ted Chinburg[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.)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 2, page 613-654
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bleher, Frauke M., and Chinburg, Ted. "Obstructions for deformations of complexes." Annales de l’institut Fourier 63.2 (2013): 613-654. <http://eudml.org/doc/275486>.

@article{Bleher2013,
abstract = {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.},
affiliation = {University of Iowa Department of Mathematics Iowa City, IA 52242-1419 (U.S.A.); University of Pennsylvania Department of Mathematics Philadelphia, PA 19104-6395 (U.S.A.)},
author = {Bleher, Frauke M., Chinburg, Ted},
journal = {Annales de l’institut Fourier},
keywords = {Versal and universal deformations; derived categories; obstructions; spectral sequences; versal and universal deformations},
language = {eng},
number = {2},
pages = {613-654},
publisher = {Association des Annales de l’institut Fourier},
title = {Obstructions for deformations of complexes},
url = {http://eudml.org/doc/275486},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Bleher, Frauke M.
AU - Chinburg, Ted
TI - Obstructions for deformations of complexes
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 2
SP - 613
EP - 654
AB - 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.
LA - eng
KW - Versal and universal deformations; derived categories; obstructions; spectral sequences; versal and universal deformations
UR - http://eudml.org/doc/275486
ER -

References

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  1. Frauke M. Bleher, Ted Chinburg, Deformations and derived categories, Ann. Institut Fourier (Grenoble) 55 (2005), 2285-2359 Zbl1138.11020MR2207385
  2. Frauke M. Bleher, Ted Chinburg, Finiteness Theorems for Deformations of Complexes., Ann. Institut Fourier (Grenoble) 63 (2013), 573-612 Zbl06193041
  3. Armand Brumer, Pseudocompact algebras, profinite groups and class formations, J. Algebra 4 (1966), 442-470 Zbl0146.04702MR202790
  4. Pierre Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448 Zbl0201.35602MR232821
  5. Pierre Gabriel, Étude infinitésimale des schémas en groupes, A. Grothendieck, SGA 3 (with M. Demazure), Schémas en groupes I, II, III (1970), 476-562, Springer-Verlag, Heidelberg Zbl0209.24201
  6. A. Grothendieck, J. Dieudonné, Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I, II, Inst. Hautes Études Sci. Publ. Math. (1961 and 1963) Zbl0122.16102MR217085
  7. Luc Illusie, Complexe cotangent et déformations. I, II, (1971 and 1972), Springer-Verlag, Berlin Zbl0224.13014MR491680
  8. B. Mazur, Deforming Galois representations, Galois groups over (Berkeley, CA, 1987) 16 (1989), 385-437, Springer Verlag, Berlin-Heidelberg-New York Zbl0714.11076MR1012172
  9. B. Mazur, Deformation theory of Galois representations, Modular Forms and Fermat’s Last Theorem (Boston, MA, 1995) (1997), 243-311, Springer Verlag, Berlin-Heidelberg-New York Zbl0901.11015MR1638481
  10. Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222 Zbl0167.49503MR217093
  11. J.-L. Verdier, Catégories derivées, P. Deligne, SGA 4.5, Cohomologie étale (1970), 262-311, Springer Verlag, Heidelberg 

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