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Kernels in the Category of Formal Group Laws

Published online by Cambridge University Press:  20 November 2018

Oleg Demchenko  and
Alexander Gurevich
Oleg Demchenko
Affiliation:
Department of Mathematics and Mechanics, St.Petersburg State University, Universitetsky pr. 28, Stary Petergof, St.Petersburg, 198504, Russia e-mail: vasja@eu.spb.ru
Alexander Gurevich
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel e-mail: gurevich@math.huji.ac.il
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Abstract

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Fontaine described the category of formal groups over the ring of Witt vectors over a finite field of characteristic $p$ with the aid of triples consisting of the module of logarithms, the Dieudonné module, and the morphism from the former to the latter. We propose an explicit construction for the kernels in this category in term of Fontaine's triples. The construction is applied to the formal norm homomorphism in the case of an unramified extension of ${{\mathbb{Q}}_{p}}$ and of a totally ramified extension of degree less or equal than $p$ . A similar consideration applied to a global extension allows us to establish the existence of a strict isomorphism between the formal norm torus and a formal group law coming from $L$ -series.

Keywords

14L05formal groupsp-divisible groupsDieudonne modulesnorm tori
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 2 , 01 April 2016 , pp. 334 - 360
Copyright
Copyright © Canadian Mathematical Society 2016

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