$K$-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.

39 pages incl. references. Comments welcome

References in corpus (3)

• On the K-theory of pullbacks
• Coassembly and the $K$-theory of finite groups
• $K$-theory of endomorphisms, the $TR$-trace, and zeta functions