On the Conductor Formula of Bloch

Parity in Bloch ’ s conductor formula in even dimension par Takeshi

For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of `adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.

Conductor formula of Bloch

Conductor is a numerical invariant of a variety over a local field measuring the wild ramification of the inertia action on the l-adic etale cohomology. In [3], S.Bloch proposes a conjectural formula, Conjecture 1.9, which we call the conductor formula of Bloch. To formulate it, he defines another numerical invariant as the degree of the self-intersection class, which is defined using the local...

Conductor formula of Bloch by Kazuya Kato and Takeshi

An embedding potential definition of channel functions

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluate...

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.