Wild sets in global function fields
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Abstract
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.
Communicated by Milan Paštéka
References
[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).10.1006/jsco.1996.0125Suche in Google Scholar
[2] Czogała, A.: Witt rings of Hasse domains of global fields, J. Algebra 244(2) (2001), 604–630.10.1006/jabr.2001.8918Suche in Google Scholar
[3] Czogała, A.—Koprowski, P.—Rothkegel, B.: Wild and even points in global function fields, Colloq. Math. 154(2) (2018), 275–294.10.4064/cm6979-1-2018Suche in Google Scholar
[4] Czogała, A.—Rothkegel, B.: Wild primes of a self-equivalence of a global function field, Acta Arith. 166(4) (2014), 335–348.10.4064/aa166-4-2Suche in Google Scholar
[5] Leep, D. B.—Wadsworth, A. R.: The Hasse norm theorem mod squares, J. Number Theory 42(3) (1992), 337–348.10.1016/0022-314X(92)90098-ASuche in Google Scholar
[6] O'Meara, O. T.: Introduction to Quadratic Forms Classics in Mathematics, Springer-Verlag, Berlin, 2000.Suche in Google Scholar
[7] Palfrey, T. C.: Density theorems for reciprocity equivalences, Ann. Math. Sil. 12 (1998), 161–172.Suche 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.Suche in Google Scholar
[9] Sharif, S.: A descent map for curves with totally degenerate semi-stable reduction, J. Théor. Nombres Bordeaux 25(1) (2013), 211–244.10.5802/jtnb.833Suche in Google Scholar
[10] Somodi, M.: A characterization of the finite wild sets of rational self-equivalences, Acta Arith. 121(4) (2006), 327–334.10.4064/aa121-4-3Suche in Google Scholar
[11] Somodi, M.: Self-equivalences of the Gaussian field, Rocky Mountain J. Math. 38(6) (2008), 2077–2089.10.1216/RMJ-2008-38-6-2077Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
Artikel in diesem Heft
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
