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2020 Tate tame symbol and the joint torsion of commuting operators
Jens Kaad, Ryszard Nest
Ann. K-Theory 5(2): 181-211 (2020). DOI: 10.2140/akt.2020.5.181

Abstract

We investigate determinants of Koszul complexes of holomorphic functions of a commuting tuple of bounded operators acting on a Hilbert space. Our main result shows that the analytic joint torsion, which compares two such determinants, can be computed by a local formula which involves a tame symbol of the involved holomorphic functions. As an application we are able to extend the classical tame symbol of meromorphic functions on a Riemann surface to the more involved setting of transversal functions on a complex analytic curve. This follows by spelling out our main result in the case of Toeplitz operators acting on the Hardy space over the polydisc.

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Jens Kaad. Ryszard Nest. "Tate tame symbol and the joint torsion of commuting operators." Ann. K-Theory 5 (2) 181 - 211, 2020. https://doi.org/10.2140/akt.2020.5.181

Information

Received: 8 February 2018; Revised: 26 July 2019; Accepted: 7 October 2019; Published: 2020
First available in Project Euclid: 11 August 2020

zbMATH: 07224512
MathSciNet: MR4113768
Digital Object Identifier: 10.2140/akt.2020.5.181

Subjects:
Primary: 32A10‎, 47A13
Secondary: 19C20, 19K56, 32C15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.5 • No. 2 • 2020
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