On the Geometry of Higher Tate SpacesPublic Deposited
This thesis is naturally split into two parts. In the first part, we develop the theory of multi- linear algebra for Tate objects over exact categories endowed with an exact tensor product. We study all possible choices of tensor product and we give a geometric interpretation of the results. In the second part, we study the derived geometry of the prestack of n-Tate objects, in the framework of connective E∞-rings. The main result is the construction of a higher determinant map from the prestack of n-Tate objects to the prestack of n-gerbes. We also give applications of this map to construct interesting central extensions of iterated loop groups, and higher Kac-Moody algebras.