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arXiv · 1408.3851

Tate tame symbol and the joint torsion of commuting operators

Jens Kaad·Ryszard Nest
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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. 2014-08-17. Tate tame symbol and the joint torsion of commuting operators. https://doi.org/10.2140/akt.2020.5.181

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