×

On Galois actions on p-power torsion points of some one-dimensional formal groups over \({\mathbb{F}}_ p[[t]]\). (English) Zbl 0644.14017

From the introduction: “We shall prove a certain theorem on the kernel of the \(p\)-adic representation \(\text{Gal}(K^{sep}/K)\to {\mathbb{Z}}^{\times}_ p\) of the absolute Galois group over \(K={\mathbb{F}}_ p(t))\) arising from a formal group of some type, including in particular the formal completion of an ordinary elliptic curve over \(K\) having good super-singular reduction.”
Reviewer: F.Baldassarri

MSC:

14L05 Formal groups, \(p\)-divisible groups
13F25 Formal power series rings
14L30 Group actions on varieties or schemes (quotients)
14H99 Curves in algebraic geometry
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Coleman, R., Division values in local fields, Invent. Math., 53, 91-116 (1979) · Zbl 0429.12010
[2] Coleman, R., Local units modulo circular units, (Proc. Amer. Math. Soc., 89 (1983)), 1-7 · Zbl 0528.12005
[3] Demazure, M., Lectures on \(P\)-Divisible Groups, (Lecture Notes in Mathematics, Vol. 302 (1972), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0247.14010
[4] Drinfeld, V. G., Coverings of \(p\)-adic symmetric regions, Functional Anal. Appl., 10, 107-115 (1976) · Zbl 0346.14010
[5] Gross, B., Ramifications in \(p\)-adic Lie extensions, Journées de Géométrie Algébrique de Rennes, 1978, Astérisque, 65, 81-102 (1979)
[6] Igusa, J., Class numbers of a definite quaternion with prime discriminant, (Proc. Nat. Acad. Sci. USA, 44 (1958)), 312-314 · Zbl 0081.03601
[7] Igusa, J., On the algebraic theory of elliptic modular functions, J. Math. Soc. Japan, 20, 96-108 (1968) · Zbl 0164.21101
[8] Katz, N., \(P\)-adic Properties of Modular Schemes and Modular Curves, (Lecture Notes in Mathematics, Vol. 350 (1973), Springer-Verlag: Springer-Verlag Berlin/New York), 69-190
[9] Lubin, J.; Tate, J., Formal complex multiplication in local fields, Ann. of Math., 81, 380-387 (1965) · Zbl 0128.26501
[10] Lubin, J.; Tate, J., Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France, 94, 49-59 (1966) · Zbl 0156.04105
[11] Washington, L., “Introduction to Cyclotomic Fields,” Graduate Texts in Mathematics (1982), Springer-Verlag: Springer-Verlag Berlin/New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.