The principal goal is generalize the field theory on spaces that admit decomposing in components that can be manageable in the complex Riemannian manifolds whose complex varieties can be part of those components called motives, creating a decomposition in the derived category of its spectrum where solutions of the field equations are defined in a hypercohomology.
2010 Ams Classification: 13D03,13D09,18G40,19D23,19D55, 24D23.
Keywords: Derived Categories, Derived Tensor Products, Étale Sheaves, Geometrical Motives Categories, Hypercohomology, Quantum Field Equations, Tensor Derived Category.
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