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Семинар им. В. А. Исковских
28 сентября 2023 г. 16:45, г. Москва, мехмат МГУ, ауд. 13-11
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An introduction to solid algebra
Ch. Brav |
Количество просмотров: |
Эта страница: | 200 |
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Аннотация:
When working with infinitely generated modules and their duals, it is
typically necessary to introduce various linear or adic topologies
in order to control duality and various completed tensor products. Such
questions arise, for example, when studying p-adic analysis in number theory
or formal schemes in algebraic geometry. Unfortunately, there is no reasonable
abelian category of topological modules, and so traditionally people have used
various ad hoc tools to do homological algebra in the topologized setting.
Recently, Clausen-Scholze have found a solution to this foundational problem,
a good abelian category of “solid modules” (more generally, “condensed
modules”). We give an elementary user guide to this theory, focusing on
concrete calculations in the category of solid modules. If time permits, we
discuss some applications to the geometry of arc and loop spaces of algebraic
varieties.
Язык доклада: английский
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