Pure and Applied Mathematics Journal
Volume 3, Issue 6-2, December 2014, Pages: 12-19
Received: Oct. 25, 2014;
Accepted: Nov. 2, 2014;
Published: Nov. 5, 2014
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Ivan Verkelov, Research Group-Tescha, Dept. of Mathematics, Baikov Institute, Baikov, Russia
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.
Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories, Pure and Applied Mathematics Journal. Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program.
Vol. 3, No. 6-2,
2014, pp. 12-19.
A. Grothendieck, On the De Rham Cohomology of algebraic varieties, Publ. Math.I.H.E.S. 29 (1966) 95-103.
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.
J. Milnor, “On spaces having the homotopy type of a CW-complex” Trans. Amer. Math. Soc. 90 (1959), 272–280.
C. Teleman, The quantization conjecture revised, Ann. Of Math. (2) 152 (2000), 1-43.
P. G. Goerss, “Topological modular forms (aftern Hopkins, Miller, and Lurie),” Available at arXiv:0910.5130v1
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.
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.
A. Efimov, V. Lunts, D. Orlov, Deformations theoryof objects in homotopy and derived categories III: Abelian categories, Available at arXiv:math/0702840v3.
V. Hinich, DG coalgebras as formal stacks, J. Pure Appl. Algebra, 162 (2001), 209-250.
V. Hinich, DG Deformations of homotopy algebras, Communications in Algebra, 32 (2004), 473-494.
B.Toën,The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (2007), no. 3, 615-667.
B.Toën, M. Vaquié, Moduli of objects in dg-categories, Ann. Sci. cole Norm. Sup. (4) 40 (2007), no. 3, 387-444.
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.
D. Ben-zvi and D. Nadler, The character theory of complex group, 5 (2011) arXiv:0904.1247v2[math.RT],
B. Fresse, Koszul duality of En-operads, Available as arXiv:0904.3123v6
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.
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.
E. Frenkel, C. Teleman, Geometric Langlands Correspondence Near Opers, Available at arXiv:1306.0876v1.