Algebra seminar - JC Tang
| Dates: | 29 October 2024 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Jiacheng Tang |
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Title: Why Condensed Abelian Groups are Better Than Topological Abelian Groups
Abstract: The category PAb of profinite abelian groups is an abelian category with many nice properties (e.g. It has enough projectives, direct products are the usual ones...), which allows us to do most of standard homological algebra. The category PAb naturally sits inside the category TAb of topological abelian groups, but TAb is not abelian, nor does it have a satisfactory theory of tensor products. On the other hand, PAb also naturally sits inside the category CondAb of "condensed abelian groups", which is an abelian category with nice properties. We will show that the embedding of profinite modules into condensed modules (actually, into "solid modules") preserves usual homological notions such Ext and Tor, so that the condensed world might be a better place to study profinite modules than the topological world.
Speaker
Jiacheng Tang
Organisation: University of Manchester
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
