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arXiv · 2009.10120

$K$-theoretic torsion and the zeta function

John R. Klein·Cary Malkiewich
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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.

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John R. Klein, Cary Malkiewich. 2020-09-21. $K$-theoretic torsion and the zeta function. https://doi.org/10.2140/akt.2022.7.77

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