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arXiv · 1508.07880

Operator ideals in Tate objects

Oliver Braunling·Michael Groechenig·Jesse Wolfson
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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.

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Oliver Braunling, Michael Groechenig, Jesse Wolfson. 2015-08-31. Operator ideals in Tate objects. https://arxiv.org/abs/1508.07880

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