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ON LOCAL FIELDS GENERATED BY DIVISION VALUES OF FORMAL DRINFELD MODULES

Part of: Discontinuous groups and automorphic forms Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  14 June 2019

HASSAN OUKHABA
HASSAN OUKHABA*
Affiliation:
Université Bourgogne Franche-Comté, Laboratoire de mathématique, 25030 Besançon cedex, France e-mail: hassan.oukhaba@univ-fcomte.fr
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Abstract

In this paper, we study some aspects of the local fields generated by division values of formal Drinfeld modules.

MSC classification

Primary: 11F85: $p$-adic theory, local fields
Secondary: 14G20: Local ground fields
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 2 , May 2020 , pp. 459 - 472
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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References

Amice, Y., Les nombres p-adiques. (French) Préface de Ch. Pisot. Collection SUP: Le Mathématicien, No. 14 (Presses Universitaires de France, Paris, 1975), 190 pp.Google Scholar
Anglès, B., On explicit reciprocity laws for the local Carlitz-Kummer symbols, J. Number Theory 78(2) (1999), 228–252.10.1006/jnth.1999.2403CrossRefGoogle Scholar
Bars, F. and Longhi, I., Coleman’s power series and Wiles’ reciprocity for rank 1 Drinfeld modules, J. Number Theory 129 (4)(2009), 789–805.CrossRefGoogle Scholar
Coleman, R. F., Division values in local fields, Invent. Math. 53 (1979), 91–116.CrossRefGoogle Scholar
Drinfeld, V. G., Elliptic modules, Mat. Sb. (N.S.) 94(136) (1974), 594–627, 656.Google Scholar
Iwasawa, K., Local class field theory, Oxford Science Publications. Oxford Mathematical Monographs (The Clarendon Press, Oxford University Press, New York, 1986).Google Scholar
Lubin, J. and Tate, J., Formal complex multiplication in local fields, Ann. Math. 81(2) (1965), 380–387.CrossRefGoogle Scholar
Rosen, M., Formal Drinfeld modules, J. Number Theory 103(2) (2003), 234–256.10.1016/S0022-314X(03)00111-2CrossRefGoogle Scholar
Washington, L. C., Introduction to cyclotomicfields, Graduate Texts in Mathematics, vol. 83, 2nd edition (Springer-Verlag, New York, 1997), xiv+487 pp. ISBN: 0-387-94762-0.Google Scholar
Wiles, A., Higher explicit reciprocity laws, Ann. Math. 107(2) (1978), 235–254.CrossRefGoogle Scholar