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Wild sets in global function fields

Alfred Czogała, Przemysław Koprowski and Beata Rothkegel
From the journal Mathematica Slovaca


Given a self-equivalence of a global function field, its wild set is the set of points where the self-equivalence fails to preserve parity of valuation. In this paper we describe structure of finite wild sets.

  1. Communicated by Milan Paštéka


[1] Bosma, W.—Cannon, J.—Playoust, C.: The Magma algebra system. I. The user language, . J. Symbolic Comput. 24(3-4) (1997), 235–265. Computational algebra and number theory (London, 1993). Search in Google Scholar

[2] Czogała, A.: Witt rings of Hasse domains of global fields, J. Algebra 244(2) (2001), 604–630. Search in Google Scholar

[3] Czogała, A.—Koprowski, P.—Rothkegel, B.: Wild and even points in global function fields, Colloq. Math. 154(2) (2018), 275–294. Search in Google Scholar

[4] Czogała, A.—Rothkegel, B.: Wild primes of a self-equivalence of a global function field, Acta Arith. 166(4) (2014), 335–348. Search in Google Scholar

[5] Leep, D. B.—Wadsworth, A. R.: The Hasse norm theorem mod squares, J. Number Theory 42(3) (1992), 337–348. Search in Google Scholar

[6] O'Meara, O. T.: Introduction to Quadratic Forms Classics in Mathematics, Springer-Verlag, Berlin, 2000. Search in Google Scholar

[7] Palfrey, T. C.: Density theorems for reciprocity equivalences, Ann. Math. Sil. 12 (1998), 161–172. Search in Google Scholar

[8] Perlis, R.—Szymiczek, K.—Conner, P. E.—Litherland, R.: Matching Witts with global fields. In: Recent Advances in Real Algebraic Geometry and Quadratic Forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991), Contemp. Math. 155, Amer. Math. Soc., Providence, RI, 1994, pp. 365–387. Search in Google Scholar

[9] Sharif, S.: A descent map for curves with totally degenerate semi-stable reduction, J. Théor. Nombres Bordeaux 25(1) (2013), 211–244. Search in Google Scholar

[10] Somodi, M.: A characterization of the finite wild sets of rational self-equivalences, Acta Arith. 121(4) (2006), 327–334. Search in Google Scholar

[11] Somodi, M.: Self-equivalences of the Gaussian field, Rocky Mountain J. Math. 38(6) (2008), 2077–2089. Search in Google Scholar

Received: 2019-01-27
Accepted: 2019-10-19
Published Online: 2020-03-10
Published in Print: 2020-04-28

© 2020 Mathematical Institute Slovak Academy of Sciences