p-adic J-homomorphisms and a product formula
Algebraic Topology
2012-01-31 v2 K-Theory and Homology
Number Theory
Abstract
One-point compactification turns real vector spaces into spheres. In homotopy theory, this transformation gets encoded in a map called the "real J-homomorphism". Here we define and investigate p-adic J-homomorphisms, which sort of turn p-adic vector spaces into spheres. Our main theorem is a product formula for these J-homomorphisms, saying what happens when you start with a rational vector space. This formula specializes to Hilbert's version of the quadratic reciprocity law after applying second homotopy groups.
Cite
@article{arxiv.1110.5851,
title = {p-adic J-homomorphisms and a product formula},
author = {Dustin Clausen},
journal= {arXiv preprint arXiv:1110.5851},
year = {2012}
}
Comments
Added Conjecture 4.5 on alternative description of J_{F_p}, otherwise just minor edits