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Liquid modules and complex analysis

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Dustin Clausen
Tue, 15/10/2019 - 14:00 - 15:00
MPIM Lecture Hall

I will report on joint work with Peter Scholze in which we define and study the concept of "liquid real vector space".  This is a replacement for the classical notion of complete locally convex real vector space, designed to have excellent formal algebraic properties while still admitting a richness of examples relevant to analytic geometry.  I will explain the basics of the liquid theory, and as an application describe how it yields a theory of "quasicoherent sheaves" on complex analytic spaces, generalizing the classical theory of coherent sheaves to the setting of infinite-dimensional fibers.

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