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Milnor-Turaev torsion and Iwasawa theory
by
Jonathan Huang
University of Maryland, College Park
There is an analogy between primes and knots, stemming from the fact that the etale fundamental group of a finite field is the profinite completion of the integers. Thus, a prime number sitting inside Spec Z behaves like a circle S1 sitting inside the sphere S3. After giving an introduction to the basic features of arithmetic topology, we will focus on the similarities between torsion invariants of Milnor and Turaev and the main conjecture in Iwasawa theory. The Alexander polynomial is analogous to the Iwasawa polynomial, and Milnor-Turaev torsion is analogous to the 'zeta element' of Kato. Finally, we will briefly discuss questions arising from refined versions of the Iwasawa main conjecture involving higher Fitting ideals.
Date received: December 22, 2013
Copyright © 2013 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbid-16.