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Newton polygons, successive minima, and different bounds for drinfeld modules of rank 2

Title
Newton polygons, successive minima, and different bounds for drinfeld modules of rank 2
Authors
Chen I.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2012
Journal Title
Proceedings of the American Mathematical Society
ISSN
0002-9939JCR Link
Citation
vol. 141, no. 1, pp. 83 - 91
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Let K = F q(T). For a Drinfeld A-module φ of rank 2 defined over C ∞, there are an associated exponential function e φ and lattice Λ φ in C∞ given by uniformization over C ∞. We explicitly determine the Newton polygons of e φ and the successive minima of Λ φ. When φ is defined over K ∞, we give a refinement of Gardeyn's bounds for the action of wild inertia at ∞ on the torsion points of φ and a criterion for the lattice field to be unramified over K ∞. If φ is in addition defined over K, we make explicit Gardeyn's bounds for the action of wild inertia at finite primes on the torsion points of φ, using results of Rosen, and this gives an explicit bound on the degree of the different divisor of division fields of φ over K. © 2012 American Mathematical Society.
DOI
10.1090/S0002-9939-2012-11300-0
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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