Deformations and derived categories

Frauke M. Bleher[1]; Ted Chinburg[2]

  • [1] University of Iowa, Department of Mathematics, Iowa City, IA 52242-1419 (USA)
  • [2] University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104-6395 (USA)

Annales de l'institut Fourier (2005)

  • Volume: 55, Issue: 7, page 2285-2359
  • ISSN: 0373-0956

Abstract

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In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology of μ p on certain affine CM ellitpic curves.

How to cite

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Bleher, Frauke M., and Chinburg, Ted. "Deformations and derived categories." Annales de l'institut Fourier 55.7 (2005): 2285-2359. <http://eudml.org/doc/116255>.

@article{Bleher2005,
abstract = {In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology of $\mu _p$ on certain affine CM ellitpic curves.},
affiliation = {University of Iowa, Department of Mathematics, Iowa City, IA 52242-1419 (USA); University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104-6395 (USA)},
author = {Bleher, Frauke M., Chinburg, Ted},
journal = {Annales de l'institut Fourier},
keywords = {Versal and universal deformations; derived categories; hypercohomology; CM elliptic curves; versal deformations; universal deformations},
language = {eng},
number = {7},
pages = {2285-2359},
publisher = {Association des Annales de l'Institut Fourier},
title = {Deformations and derived categories},
url = {http://eudml.org/doc/116255},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Bleher, Frauke M.
AU - Chinburg, Ted
TI - Deformations and derived categories
JO - Annales de l'institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 7
SP - 2285
EP - 2359
AB - In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology of $\mu _p$ on certain affine CM ellitpic curves.
LA - eng
KW - Versal and universal deformations; derived categories; hypercohomology; CM elliptic curves; versal deformations; universal deformations
UR - http://eudml.org/doc/116255
ER -

References

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