Derived Tensor Products and Their Applications

In this research we studied t he tensor product on derived categories of Étale sheaves with transfers considering as fundamental, the tensor product of categories X ⊗ Y ¼ X (cid:2) Y , on the category Cor k , (finite correspondences category) by under-standing it to be the product of the underlying schemes on k . Although, to this is required to build a total tensor product on the category PST( k ), where this construction will be useful to obtain generalizations on derived categories using pre-sheaves and contravariant and covariant functors on additive categories to define the exactness of infinite sequences and resolution of spectral sequences. Some concrete applications are given through a result on field equations solution.