$K$-theoretic torsion and the zeta function
Abstract
We generalize to higher algebraic $K$-theory an identity (originally due to Milnor) that relates the Reidemeister torsion of an infinite cyclic cover to its Lefschetz zeta function. Our identity involves a higher torsion invariant, the endomorphism torsion, of a parametrized family of endomorphisms as well as a higher zeta function of such a family. We also exhibit several examples of families of endomorphisms having non-trivial endomorphism torsion.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.10120
- arXiv:
- arXiv:2009.10120
- Bibcode:
- 2020arXiv200910120K
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Topology;
- 19J10;
- 57Q10
- E-Print:
- 39 pages incl. references. Comments welcome