Tensor Triangulated Category to Quantum Version of Motivic Cohomology on Etale Sheaves

The tensor structure of triangulated categories will be considered in derivedcategories of étale sheaves with transfers performed the tensor product of categories in the finite correspondences category considering the product underlying of schemes on a field A total tensor product on the category is required to obtain the generalizations on derived categories using pre-sheaves, contravariant and covariant functors on additive categories of the type or to determine the exactness of infinite sequences of cochain complexes and resolution of spectral sequences. Then by a motives algebra, which inherits the generalized tensor product of , is defined a triangulated category whose motivic cohomology is a hypercohomology from the category , which has implications in the geometrical motives applied to bundle of geometrical stacks in field theory. Then are considered the motives in the hypercohomoloy to the category A fundamental result in a past research was the creation of lemma that incorporates a 2-simplicial decomposition of in four triangular diagrams of derived categories from the category, this was with the goal to evidence the tensor structure of Now in this research we consider a theorem that relates the hypercohomology groups obtained with the spectrum through the its singular homology taking components and the homotopy in the action of the symmetric group on the derived category Finally will give a crystallographic space-time model of simplicial type from the microscopic aspects that define it, and will be established under the dualities in field theory and the hypercohomology Nisnevich groups that the vertices in decomposition of the space are equivalent to the field waves, for example gravitational waves.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.