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BAD FIELDS WITH TORSION

  • JUAN DIEGO CAYCEDO (a1) and MARTIN HILS (a2) (a3)

Abstract

We extend the construction of bad fields of characteristic zero to the case of arbitrary prescribed divisible green torsion.

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[1]Baudisch, Andreas, Hils, Martin, Martin Pizarro, Amador, and Wagner, Frank O., Die böse Farbe. Journal of the Institute of Mathematics of Jussieu, vol. 8 (2009), no. 3, pp. 415443.
[2]Bays, Martin, Gavrilovich, Misha, and Hils, Martin, Some definability results in abstract Kummer theory. International Mathematics Research Notices, Apr 2013, rnt057.
[3]Caycedo, Juan Diego, em Expansions of 1-dimensional algebraic groups by a predicate for a subgroup, D.Phil. Thesis, University of Oxford, Oxford, 2011.
[4]Hils, Martin, Generic automorphisms and green fields. Journal of the London Mathematical Society (2), vol. 85 (2012), no. 2, pp. 223244.
[5]Laurent, Michel, Équations diophantiennes exponentielles. Inventiones mathematicae, vol. 78 (1984), no. 2, pp. 299327.
[6]Poizat, Bruno, L’égalité au cube, this Journal, vol. 66 (2001), no. 4, pp. 1647–1676.
[7]Wagner, Frank O., Bad fields in positive characteristic. Bulletin of Symbolic Logic, vol. 35 (2003), pp. 499502.
[8]Zilber, Boris, Exponential sums equations and the Schanuel conjecture. Journal of the London Mathematical Society (2), vol. 65 (2002), no. 1, pp. 2744.
[9]Zilber, Boris, Covers of the multiplicative group of an algebraically closed field of characteristic zero. Journal of the London Mathematical Society (2), vol. 74 (2006), no. 1, pp. 4158.
[10]Zilber, Boris, The theory of exponential sums, preprint, 2011.

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