A characterization of the finite wild sets of rational self-equivalences

Wild and even points in global function fields

“…belongs to the subgroup 2 Pic K). On implication of this theorem, still holds even when we increase the number of points, this way we obtain a complete counterpart (Theorem 4.8) for function fields of the results from [Som06,Som08,CR14]. These two results establish a direct link between the property of being wild (for some-self equivalence) and 2-divisibility in the Picard group of K. For this reason, we develop in Section 3 some criteria for the class of a point p ∈ X to be 2-divisible in the group Pic K. In particular, we show (cf.…”

“…Given a self-equivalence of a global field K, a prime p of K is called tame if ord p λ ≡ ord T p tλ (mod 2) for all λ ∈ K. Otherwise p is called wild. Few years ago, M. Somodi gave a full characterization all finite sets of wild primes in Q (see [Som06]) and in Q(i) (see [Som08]). His results were recently generalized to a broad class of number fields by two of the authors of this article (for details see [CR14]).…”

Wild sets in global function fields

“…The problem was investigated first by T. Palfrey in [6]. Next, M. Somodi in [9,10] completely described the structure of wild sets of Q and Q [i]. Subsequently two of the present authors obtained a partial characterization of wild sets of number fields.…”

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

“…In the case of a Hilbert equivalence which is not tame it is natural to ask what the wild set of this equivalence could be. In [13] Somodi estimated the size of the wild set of Hilbert equivalence of degree 2, whereas in [14] and [15] he gave a description of the wild set of Hilbert self-equivalence of degree 2 of the rational number field Q as well as the Gaussian field Q(i). Somodi's results were generalized to a wider family of number fields in [7].…”