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Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

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arxiv 1706.03336 v1 pith:YMQCCPYK submitted 2017-06-11 math.NT math-phmath.MP

Hee-Joong Chung , Dohyeong Kim , Minhyong Kim , George Pappas , Jeehoon Park , Hwajong Yoo This is my paper
classification math.NTmath-phmath.MP
keywords arithmeticlinkingnumberstheoryabeliananaloguechern-simonscompute
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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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