Chromatic polylogarithms

Beilinson's conjectures predict that special values of L-functions are periods. In the case of number fields, Zagier verified numerically that these periods should arise more precisely as special values of polylogarithms. Following Beilinson's philosophy of regulators, this suggested that polylogarithms should come from motivic cohomology, and some instances of these "motivic polylogarithms" were indeed first constructed by Beilinson, Deligne, and Soulé. In this talk, I want to explain a new construction of the polylogarithm functions in algebraic K-theory and in motivic cohomology, which naturally recovers the motivic classes of Beilinson--Deligne--Soulé as a special case, and which also suggests a surprising relation to chromatic homotopy theory. This is a joint work in progress with Arpon Raksit, partly based on a joint work with Benjamin Antieau, Federico Binda, and Brian Shin.

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