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arxiv: 1904.09966 · v2 · submitted 2019-04-22 · 🧮 math.AG · math.AT· math.CT

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Pyknotic objects, I. Basic notions

Clark Barwick , Peter Haine
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classification 🧮 math.AG math.ATmath.CT
keywords objectspyknoticbasictheoryadditionalalgebraappearsarticle
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Pyknotic objects are (hyper)sheaves on the site of compacta. These provide a convenient way to do algebra and homotopy theory with additional topological information present. This appears, for example, when trying to contemplate the derived category of a local field. In this article, we present the basic theory of pyknotic objects, with a view to describing a simple set of everyday examples.

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  1. Lectures on Condensed Mathematics

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    Lecture notes introducing condensed mathematics as a framework for topology in algebraic and analytic settings.