Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories

Ivan Verkelov

doi:doi:10.11648/j.pamj.s.2014030602.13

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Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories

Ivan Verkelov

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6-2)

Received: 25 October 2014 Accepted: 2 November 2014 Published: 5 November 2014

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Abstract

The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 6-2) This article belongs to the Special Issue Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program
DOI	10.11648/j.pamj.s.2014030602.13
Page(s)	12-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Deformed Category, E∞— Rings, Formal Moduli Problem, Koszul Duality, Non-Commutative Geometry

References

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[2]	M. Kontsevich, Y. Soibelman, Deformations of algebras over operads and the Deligne conjecture, Conference Moshe Flato 1999, Vol 1 (Dijon), 255-307, Math. Phys. Stud., 21, Kluwer Acad. Publ., Dordrecht, 2000.
[3]	J. Milnor, “On spaces having the homotopy type of a CW-complex” Trans. Amer. Math. Soc. 90 (1959), 272–280.
[4]	C. Teleman, The quantization conjecture revised, Ann. Of Math. (2) 152 (2000), 1-43.
[5]	P. G. Goerss, “Topological modular forms (aftern Hopkins, Miller, and Lurie),” Available at arXiv:0910.5130v1
[6]	A. Efimov, V. Lunts, D. Orlov, Deformations theoryof objects in homotopy and derived categories I: General Theory, Adv. Math. 222 (2009), no. 2, 359-401.
[7]	A. Efimov, V. Lunts, D. Orlov, Deformations theoryof objects in homotopy and derived categories II: Pro-representability of the deformation functor, Available at arXiv:math/0702839v3.
[8]	A. Efimov, V. Lunts, D. Orlov, Deformations theoryof objects in homotopy and derived categories III: Abelian categories, Available at arXiv:math/0702840v3.
[9]	V. Hinich, DG coalgebras as formal stacks, J. Pure Appl. Algebra, 162 (2001), 209-250.
[10]	V. Hinich, DG Deformations of homotopy algebras, Communications in Algebra, 32 (2004), 473-494.
[11]	B.Toën,The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (2007), no. 3, 615-667.
[12]	B.Toën, M. Vaquié, Moduli of objects in dg-categories, Ann. Sci. cole Norm. Sup. (4) 40 (2007), no. 3, 387-444.
[13]	B.Toën, G. Vezzosi, From HAG to derived moduli stacks. Axiomatic, enriched and motivic homotopy theory, 173-216. NATO Sci. Ser II, Math. Phys. Chem., 131, Kluwer Acad. Publ. Dordrecht, 2004.
[14]	D. Ben-zvi and D. Nadler, The character theory of complex group, 5 (2011) arXiv:0904.1247v2[math.RT],
[15]	B. Fresse, Koszul duality of En-operads, Available as arXiv:0904.3123v6
[16]	F. Bulnes, Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory, Advances in Pure Mathematics 3 (2) (2013) 246-253. doi: 10.4236/apm.2013.32035.
[17]	F. Bulnes, Cohomology of Moduli Spaces in Differential Operators Classification to the Field Theory (II), in: Proceedings of Function Spaces, Differential Operators and Non-linear Analysis., 2011, Tabarz Thur, Germany, Vol. 1 (12) pp001-022.
[18]	E. Frenkel, C. Teleman, Geometric Langlands Correspondence Near Opers, Available at arXiv:1306.0876v1.

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APA Style

Ivan Verkelov. (2014). Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure and Applied Mathematics Journal, 3(6-2), 12-19. https://doi.org/10.11648/j.pamj.s.2014030602.13

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ACS Style

Ivan Verkelov. Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure Appl. Math. J. 2014, 3(6-2), 12-19. doi: 10.11648/j.pamj.s.2014030602.13

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AMA Style

Ivan Verkelov. Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure Appl Math J. 2014;3(6-2):12-19. doi: 10.11648/j.pamj.s.2014030602.13

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@article{10.11648/j.pamj.s.2014030602.13,
  author = {Ivan Verkelov},
  title = {Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6-2},
  pages = {12-19},
  doi = {10.11648/j.pamj.s.2014030602.13},
  url = {https://doi.org/10.11648/j.pamj.s.2014030602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.13},
  abstract = {The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.},
 year = {2014}
}

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TY  - JOUR
T1  - Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
AU  - Ivan Verkelov
Y1  - 2014/11/05
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2014030602.13
DO  - 10.11648/j.pamj.s.2014030602.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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EP  - 19
PB  - Science Publishing Group
SN  - 2326-9812
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AB  - The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.
VL  - 3
IS  - 6-2
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Author Information

Ivan Verkelov

Research Group-Tescha, Dept. of Mathematics, Baikov Institute, Baikov, Russia

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APA Style

Ivan Verkelov. (2014). Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure and Applied Mathematics Journal, 3(6-2), 12-19. https://doi.org/10.11648/j.pamj.s.2014030602.13

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ACS Style

Ivan Verkelov. Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure Appl. Math. J. 2014, 3(6-2), 12-19. doi: 10.11648/j.pamj.s.2014030602.13

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AMA Style

Ivan Verkelov. Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories. Pure Appl Math J. 2014;3(6-2):12-19. doi: 10.11648/j.pamj.s.2014030602.13

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@article{10.11648/j.pamj.s.2014030602.13,
  author = {Ivan Verkelov},
  title = {Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6-2},
  pages = {12-19},
  doi = {10.11648/j.pamj.s.2014030602.13},
  url = {https://doi.org/10.11648/j.pamj.s.2014030602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.13},
  abstract = {The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
AU  - Ivan Verkelov
Y1  - 2014/11/05
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2014030602.13
DO  - 10.11648/j.pamj.s.2014030602.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 12
EP  - 19
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2014030602.13
AB  - The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.
VL  - 3
IS  - 6-2
ER  -

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