Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formu...

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Hlavní autoři: Chung, H, Kim, D, Kim, M, Pappas, G, Park, J, Yoo, H
Médium: Journal article
Vydáno: Oxford University Press 2017
Popis
Shrnutí:Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers.