精确类别中的泰特对象(附Jan \vS\vtov\ \ \vcek和Jan Trlifaj的附录)

O. Braunling, M. Groechenig, J. Wolfson
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引用次数: 23

摘要

我们在一个精确范畴中研究基本的Tate对象。我们将初等Tate对象的范畴描述为可容许Ind-Pro对象的最小子范畴,它包含了可容许ind -对象和可容许pro -对象的范畴,并且在扩展下是封闭的。我们将Beilinson的Tate模块方法与Drinfeld的方法进行比较。我们建立了幂等完全精确范畴上初等Tate对象的Sato Grassmannian的几个性质(例如它是一个有向偏集)。最后,我们对n-Tate模和n维ad {e}进行了简要的处理。在J. \v \vtov\ \i\vcek和J. Trlifaj的附录中,利用有限生成投影模范畴中可容许ind对象范畴的幂等补全,确定了平面Mittag-Leffler模的范畴。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)
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 ad\`{e}les. An appendix due to J. \vS\vtov\'\i\vcek 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.
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