Wild sets in global function fields

Czogała, Alfred; Koprowski, Przemysław; Rothkegel, Beata

doi:10.1515/ms-2017-0349

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Cited by 3 publications

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“…Like in the case of polynomials this relation is symmetric (see Proposition 14) but not transitive (see [2,Remark 3]). It is known (see [2,Proposition 4.5] and [1,Proposition 4.7]) that the relation ⌣ controls the formation of bigger wild sets of self-equivalences of K.…”

Section: Introductionmentioning

confidence: 99%

Graph of even points on an arithmetic curve

Czogała¹,

Koprowski²

2019

Preprint

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We show that the points of a global function field, whose classes are 2-divisible in the Picard group, form a connected graph, with the incidence relation generalizing the well known quadratic reciprocity law. We prove that for every global function field the dimension of this graph is precisely 2. In addition we develop an analog of global square theorem that concerns points 2-divisible in the Picard group.

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Section: Introductionmentioning

confidence: 99%

Graph of even points on an arithmetic curve

Czogała¹,

Koprowski²

2019

Preprint

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“…Let K = F q (X) be an arbitrary global function field of characteristic = 2. A generalization of the relation to the set of points (primes) of K, whose classes are 2-divisible in the Picard group Pic X, was introduced in [2] and further investigated in [3,1]. We should emphasize the fact that on such points the relation is defined canonically.…”

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confidence: 99%