Tate tame symbol and the joint torsion of commuting operators

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Tate tame symbol and the joint torsion of commuting operators. / Kaad, Jens; Nest, Ryszard.

I: Annals of K-Theory, Bind 5, Nr. 2, 2020, s. 181-211.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Kaad, J & Nest, R 2020, 'Tate tame symbol and the joint torsion of commuting operators', Annals of K-Theory, bind 5, nr. 2, s. 181-211. https://doi.org/10.2140/akt.2020.5-2

APA

Kaad, J., & Nest, R. (2020). Tate tame symbol and the joint torsion of commuting operators. Annals of K-Theory, 5(2), 181-211. https://doi.org/10.2140/akt.2020.5-2

Vancouver

Kaad J, Nest R. Tate tame symbol and the joint torsion of commuting operators. Annals of K-Theory. 2020;5(2):181-211. https://doi.org/10.2140/akt.2020.5-2

Author

Kaad, Jens ; Nest, Ryszard. / Tate tame symbol and the joint torsion of commuting operators. I: Annals of K-Theory. 2020 ; Bind 5, Nr. 2. s. 181-211.

Bibtex

@article{ce0f4245095d4c2eb699ad3bce4787dd,
title = "Tate tame symbol and the joint torsion of commuting operators",
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. ",
author = "Jens Kaad and Ryszard Nest",
year = "2020",
doi = "10.2140/akt.2020.5-2",
language = "English",
volume = "5",
pages = "181--211",
journal = "Annals of K-Theory",
issn = "2379-1683",
publisher = "K-Theory Foundation, Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Tate tame symbol and the joint torsion of commuting operators

AU - Kaad, Jens

AU - Nest, Ryszard

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

U2 - 10.2140/akt.2020.5-2

DO - 10.2140/akt.2020.5-2

M3 - Journal article

VL - 5

SP - 181

EP - 211

JO - Annals of K-Theory

JF - Annals of K-Theory

SN - 2379-1683

IS - 2

ER -

ID: 257742966