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.

Last modified

• 04/15/2019

Creator

• Aron Alexandre Heleodoro

DOI

• https://doi.org/10.21985/N26Z01

Subject

• Mathematics

Keyword

• Tate objects
• tensor product
• central extension
• determinant

Date created

• 2018-01-01

Resource type

• Dissertation

Rights statement

• In Copyright