#### Hecke Categories Cocycles as Field Equations Solutions on L-Holomorphic Bundles

###### Autor: Francisco Bulnes Aguirre

###### We consider certain derived categories on coherent D-modules to construct a moduli space of equivalences between objects of a complex holomorphic bundle and a sheaf of coherent D- modules, which are determined for generalization of a certain integral transform in the derived categories level. Their images are Hecke categories on L- holomorphic bundles. These co-cycles represent solutions of the ﬁeld equations. Their ramiﬁcations can be identiﬁed as degenerated cycles corresponding to orbits of coherent D-modules of certain Moduli space that can be induced by an appropriate Zuckerman functor obtained by a generalized Penrose transform developed on derived categories of a moduli space of flat connections sheaves. Likewise, are obtained classes of objects in a moduli space of ﬁelds where the Lagrangians are submanifolds of a Calabi-Yau manifold and have a ﬁeld theory re-interpretation as D-branes as P- modules, obtaining solution classes to field equations starting from the wave equation.