Finiteness Theorems 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 573-612
  • ISSN: 0373-0956

Abstract

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We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of G -modules that is strictly perfect over the associated versal deformation ring.

How to cite

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Bleher, Frauke M., and Chinburg, Ted. "Finiteness Theorems for Deformations of Complexes." Annales de l’institut Fourier 63.2 (2013): 573-612. <http://eudml.org/doc/275614>.

@article{Bleher2013,
abstract = {We consider deformations of bounded complexes of modules for a profinite group $G$ over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of $G$-modules that is strictly perfect over the associated versal deformation ring.},
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; finiteness questions; tame fundamental groups; versal and universal deformations},
language = {eng},
number = {2},
pages = {573-612},
publisher = {Association des Annales de l’institut Fourier},
title = {Finiteness Theorems for Deformations of Complexes},
url = {http://eudml.org/doc/275614},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Bleher, Frauke M.
AU - Chinburg, Ted
TI - Finiteness Theorems 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 - 573
EP - 612
AB - We consider deformations of bounded complexes of modules for a profinite group $G$ over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of $G$-modules that is strictly perfect over the associated versal deformation ring.
LA - eng
KW - Versal and universal deformations; derived categories; finiteness questions; tame fundamental groups; versal and universal deformations
UR - http://eudml.org/doc/275614
ER -

References

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  1. Frauke M. Bleher, Ted Chinburg, Deformations and derived categories, C. R. Math. Acad. Sci. Paris 334 (2002), 97-100 Zbl1079.11027MR1885087
  2. Frauke M. Bleher, Ted Chinburg, Deformations and derived categories, Ann. Inst. Fourier (Grenoble) 55 (2005), 2285-2359 Zbl1138.11020MR2207385
  3. Frauke M. Bleher, Ted Chinburg, Obstructions for deformations of complexes, Ann. Inst. Fourier (Grenoble) 63 (2013), 613-654 Zbl06193042
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  7. Alexander Grothendieck, Jacob P. Murre, The tame fundamental group of a formal neighbourhood of a divisor with normal crossings on a scheme, (1971), Springer-Verlag, Berlin Zbl0216.33001MR316453
  8. Robin Hartshorne, Algebraic geometry, (1977), Springer-Verlag, New York Zbl0531.14001MR463157
  9. Mark Kisin, Moduli of finite flat group schemes, and modularity, Ann. of Math. (2) 170 (2009), 1085-1180 Zbl1201.14034MR2600871
  10. Michel Lazard, Groupes analytiques p -adiques, Inst. Hautes Études Sci. Publ. Math. (1965), 389-603 Zbl0139.02302MR209286
  11. B. Mazur, Deforming Galois representations, Galois groups over (Berkeley, CA, 1987) 16 (1989), 385-437, Springer, New York Zbl0714.11076MR1012172
  12. Barry Mazur, An introduction to the deformation theory of Galois representations, Modular forms and Fermat’s last theorem (Boston, MA, 1995) (1997), 243-311, Springer, New York Zbl0901.11015MR1638481
  13. Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222 Zbl0167.49503MR217093
  14. Alexander Schmidt, Tame coverings of arithmetic schemes, Math. Ann. 322 (2002), 1-18 Zbl1113.14022MR1883386
  15. Bart de Smit, Hendrik W. Lenstra, Explicit construction of universal deformation rings, Modular forms and Fermat’s last theorem (Boston, MA, 1995) (1997), 313-326, Springer, New York Zbl0907.13010MR1638482
  16. J.-L. Verdier, Catégories derivées, P. Deligne, SGA 4.5, Cohomologie étale (1970), 262-311, Springer-Verlag, Heidelberg 

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