EVENT DETAILS AND ABSTRACT

Title: A homotopical refinement of the quadratic reciprocity law
Speaker: Dustin Clausen
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Hilbert reinterpreted the quadratic reciprocity law as a "product formula" relating certain "Hilbert symbols" attached to the various completions of the rational numbers (namely, the reals R as well as all the p-adics Q_p). In modern terms these Hilbert symbols can be viewed as homomorphisms from the 2nd algebraic K-groups of these various completions to the group of order two. Here we'll explain how to generalize these Hilbert symbols, as well as the product formula relating them, to the level of the algebraic K-theory spectra involved. At the reals R the proposed generalization is given by the real J-homomorphism, so this involves defining "p-adic J-homomorphisms" and demonstrating their connection (and analogy) with the real J-homomorphism.