Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T12:53:41.149Z Has data issue: false hasContentIssue false

ON LOCAL FIELDS GENERATED BY DIVISION VALUES OF FORMAL DRINFELD MODULES

Published online by Cambridge University Press:  14 June 2019

HASSAN OUKHABA*
Affiliation:
Université Bourgogne Franche-Comté, Laboratoire de mathématique, 25030 Besançon cedex, France e-mail: [email protected]

Abstract

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

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 228252.10.1006/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), 789805.CrossRefGoogle Scholar
Coleman, R. F., Division values in local fields, Invent. Math. 53 (1979), 91116.CrossRefGoogle Scholar
Drinfeld, V. G., Elliptic modules, Mat. Sb. (N.S.) 94(136) (1974), 594627, 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), 380387.CrossRefGoogle Scholar
Rosen, M., Formal Drinfeld modules, J. Number Theory 103(2) (2003), 234256.10.1016/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), 235254.CrossRefGoogle Scholar