Tate tame symbol and the joint torsion of commuting operators
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- Tate tame symbol and the joint torsion of commuting operators
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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.
Originalsprog | Engelsk |
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Tidsskrift | Annals of K-Theory |
Vol/bind | 5 |
Udgave nummer | 2 |
Sider (fra-til) | 181-211 |
ISSN | 2379-1683 |
DOI | |
Status | Udgivet - 2020 |
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