Torsion elements of order 𝑝2 in the Nottingham group
نویسندگان
چکیده
منابع مشابه
Torsion in the Nottingham group
From local class-field theory and higher ramification theory one gets a classification up to conjugacy of the torsion elements of arbitrary order in the Nottingham group over a finite field, in terms of continuous characters on the multiplicative group of principal units in the ring of formal power series over the field. An essential part of this classification is to partition the torsion eleme...
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Let p ≥ 5 be a prime number. We prove that the abstract commensurator of the Nottingham group N (Fp) coincides with its automorphism group, which is known to be a finite extension of N (Fp). As a corollary we deduce that the Nottingham group cannot be embedded as an open subgroup of a topologically simple group.
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1. Introduction. If we wish to write the equations of curves of genus 1 that give elements of the Shafarevich-Tate group of an elliptic curve over a number field K, a choice of ways is open to us. For example, if the element in question is of order 3 the curve of genus 1 corresponding to it occurs as a smooth plane cubic curve over K. In a recent article [C-M] we raised the question of when one...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2020
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2019-0114