Moscow Mathematical Journal
Volume 16, Issue 3, July–September 2016 pp. 433–504.
Tate Objects in Exact Categories We study elementary Tate objects in an exact category. We
characterize the category of elementary Tate objects as the smallest subcategory 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. 2010 Math. Subj. Class. 18E10 (Primary), 11R56, 13C60 (Secondary).
(with an appendix by Jan Stovicek and Jan Trlifaj)
Authors:
Oliver Braunling (1), Michael Groechenig (2), and Jesse Wolfson (3)
Author institution:(1) Department of Mathematics, Universität Freiburg
(2) Department of Mathematics, Imperial College London
(3) Department of Mathematics, University of Chicago
Summary:
Keywords: Drinfeld bundle, local compactness, Tate extension, categorical Sato Grassmannian, higher adèles.
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