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Abelian arithmetic Chern-Simons theory and arithmetic linking numbers (1706.03336v1)
Published 11 Jun 2017 in math.NT, math-ph, and math.MP
Abstract: 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.
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