Pure and Applied Mathematics Journal 2014; 3(6-2): 6-11 Published online October 23, 2014 (http://www.sciencepublishinggroup.com/j/pamj) doi: 10.11648/j.pamj.s.2014030602.12 ISSN: 2326-9790 (Print); ISSN: 2326-9812 (Online) Coverings and axions: Topological characterizing of the energy coverings in space-time Mario Ramírez 1 , Luis Ramírez 2 , Oscar Ramírez 3 , Francisco Bulnes 4, * 1 Dept. of Mathematics, ESIME-Azcapotzalco, Mexico City, Mexico 2 Dept. of Mathematics, UNAM-FES-Aragón, Mexico City, Mexico 3 Dept. of Mathematics, UNAM-FES-Acatlán, Mexico City, Mexico 4 Research Dept. in Mathematics and Eng., TESCHA, Chalco, Mexico Email address: mramirezf@ipn.mx (M. Ramírez), elluis_47@yahoo.com.mx (L. Ramírez), intermezzoadagio@hotmail.com.mx (O. Ramírez), francisco.bulnes@tesch.edu.mx (F. Bulnes) To cite this article: Mario Ramírez, Luis Ramírez, Oscar Ramírez, Francisco Bulnes. Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time. 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. 6-11. doi: 10.11648/j.pamj.s.2014030602.12 Abstract: Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their spectrum that is characterized by their wrapping energy. Keywords: Axion, Diffeomorphism, Spectrum, Universal Covering, Wrapping Energy 1. Introduction The study begins with a interesting question, how to arrive to a definition of time or energy? We know that the concept with that works the physics and after the mathematics not start of the nothing, are abstractions realized to start of the observation and after interpretation of all that us is sensible. The man has had as concerns the description of that happens in the nature and has mean importance the time and the energy. To arrive to a definition not has been possible, the intent have been probable, nevertheless, the advances in topological theory of strings and - D branes, furthermore of the obtaining of concepts as curvature and torsion energy, inclusive used in some dissertations as [1] to their application of devices to curvature measure of quantum gravity have done probable the crating of a theory at least to conjecture level of the equivalence of these concepts. Possibly and with the development of photonic and spintronic devices (energy and time established in the QFT through bosons and spins) can be demonstrated under observational facts such theory. To the question, is possible to establish equivalence between energy and time? Could have as immediate response and categorist no! Nevertheless re-evaluating the question in the context of the ramified field, could establish an equivalence, not in a purely algebraic sense and the continuous applications only, but, if for certain differential applications that born of several dualities (for example, the Langlands duality [2, 3]) and that are deformable images of certain applications between of differential operators in a holomorphic context and whose actions on said elements (ramifications) are actions from of loop groups obtained in the construction of cycles of the space-time [3]. 2. Spectrum of the Commutative Rings Let X , be a scheme [4], for example, the scheme given from the derived categories , X D whose sheaves let , I be coherent sheaves of ideals on X , then the transformation that we define is the morphism , ~ : X X → π such that , ~ 1 X O I - π is an invertible sheaf. Here X ~ O , is the structure of the sheaf of X ~ . Likewise, morphisms from schemes to affine schemes are completely understood in terms of ring homomorphisms by the following contravariant adjoint pair: For every scheme X , and every commutative ring , A we have a natural equivalence Schemes CRing Hom ( ,Spec( )) Hom (, ( )) X X A AO X 2245 (1)