Affiliation:
1. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8551, Japan
Abstract
In their 2019 paper, Lee and Park presented a formula for the arithmetic Chern–Simons invariant. This formula gives a relation between this invariant and the local Hasse invariants at certain finite primes. Given a number field having real embeddings, we present alternative formulas to give relations between the arithmetic Chern–Simons invariant and the local Hasse invariants at certain primes including all real ones. As an application, we propose a new problem which concerns the existence of a certain [Formula: see text]-cocycle. If the answer to this problem is positive, the obtained statement is an analogue of the Albert–Brauer–Hasse–Noether theorem.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory