Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms

Francisco Bulnes

Research Department in Mathematics and Engineering, Tecnológico de Estudios Superiores de Chalco, Chalco, Mexico.

DOI: 10.4236/apm.2014.46034                

Abstract

Some derived categories and their deformed versions are used to develop a theory of the ramifications of field studied in the geometrical Langlands program to obtain the correspondences between moduli stacks and solution classes represented cohomologically under the study of the kernels of the differential operators studied in their classification of the corresponding field equations. The corresponding D-modules in this case may be viewed as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform) naturally arising in the framework of conformal field theory. Inside the geometrical Langlands correspondence and in their cohomological context of strings can be established a framework of the space-time through the different versions of the Penrose transforms and their relation between them by intertwining operators (integral transforms that are isomorphisms between cohomological spaces of orbital spaces of the space-time), obtaining the functors that give equivalences of their corresponding categories.(For more information,please refer to the PDF version.)

Keywords

Geometrical Langlands Correspondence, Hecke Categories, Moduli Stacks, Penrose Transforms, Quasi-Coherent Sheaves

Conflicts of Interest

The authors declare no conflicts of interest.

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