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.
In: Annals of K-Theory, Vol. 5, No. 2, 2020, p. 181-211.Research output: Contribution to journal › Journal article › Research › peer-review
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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