The Chern character and categorification
Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019
Location: SLMath: Eisenbud Auditorium
Chern character
categorification
14G12 - Hasse principle, weak and strong approximation, Brauer-Manin obstruction [See also 14F22]
18B20 - Categories of machines, automata [See also 03D05, 68Qxx]
18M65 - Non-symmetric operads, multicategories, generalized multicategories
15-Scherotzke
The Chern character is a central construction which appears in topology, representation theory and algebraic geometry. In algebraic topology it is for instance used to probe algebraic K-theory which is notoriously hard to compute, in representation theory it takes the form of classical character theory. Recently, Toen and Vezzosi suggested a construction, using derived algebraic geometry, which allows to unify the various Chern characters. We will categorify this Chern character. In the categorified picture algebraic K-theory is replaced by the category of non-commutative motives. It turns out that the categorified Chern character has many interesting applications. For instance we show that the DeRham realisation functor is of non-commutative origin.
Notes
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15-Scherotzke
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