|
This article is cited in 22 scientific papers (total in 22 papers)
Tate objects in exact categories (with an appendix by Jan Šťovíček and Jan Trlifaj)
Oliver Braunlinga, Michael Groechenigb, Jesse Wolfsonc a Department of Mathematics, Universität Freiburg
b Department of Mathematics, Imperial College London
c Department of Mathematics, University of Chicago
Abstract:
We study elementary Tate objects in an exact category. We characterize the category of elementary Tate objects as the smallest sub-category of admissible Ind-Pro objects which contains the categories of admissible Ind-objects and admissible Pro-objects, and which is closed under extensions. We compare Beilinson's approach to Tate modules to Drinfeld's. We establish several properties of the Sato Grassmannian of an elementary Tate object in an idempotent complete exact category (e.g., it is a directed poset). We conclude with a brief treatment of $n$-Tate modules and $n$-dimensional adèles.
An appendix due to J. Šťovíček and J. Trlifaj identifies the category of flat Mittag-Leffler modules with the idempotent completion of the category of admissible Ind-objects in the category of finitely generated projective modules.
Key words and phrases:
Drinfeld bundle, local compactness, Tate extension, categorical Sato Grassmannian, higher adèles.
Received: May 26, 2014; in revised form January 19, 2016
Citation:
Oliver Braunling, Michael Groechenig, Jesse Wolfson, “Tate objects in exact categories (with an appendix by Jan Šťovíček and Jan Trlifaj)”, Mosc. Math. J., 16:3 (2016), 433–504
Linking options:
https://www.mathnet.ru/eng/mmj606 https://www.mathnet.ru/eng/mmj/v16/i3/p433
|
Statistics & downloads: |
Abstract page: | 386 | References: | 54 |
|