Operator ideals in Tate objects
Algebraic Geometry
2017-03-31 v1 Rings and Algebras
Abstract
Tate's central extension originates from 1968 and has since found many applications to curves. In the 80s Beilinson found an n-dimensional generalization: cubically decomposed algebras, based on ideals of bounded and discrete operators in ind-pro limits of vector spaces. Kato and Beilinson independently defined '(n-)Tate categories' whose objects are formal iterated ind-pro limits in general exact categories. We show that the endomorphism algebras of such objects often carry a cubically decomposed structure, and thus a (higher) Tate central extension. Even better, under very strong assumptions on the base category, the n-Tate category turns out to be just a category of projective modules over this type of algebra.
Keywords
Cite
@article{arxiv.1508.07880,
title = {Operator ideals in Tate objects},
author = {Oliver Braunling and Michael Groechenig and Jesse Wolfson},
journal= {arXiv preprint arXiv:1508.07880},
year = {2017}
}