Computations with Witt vectors of length 3

Luís R. A. Finotti[1]

  • [1] Department of Mathematics University of Tennessee Knoxville, TN 37996, USA

Journal de Théorie des Nombres de Bordeaux (2011)

  • Volume: 23, Issue: 2, page 417-454
  • ISSN: 1246-7405

Abstract

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In this paper we describe how to perform computations with Witt vectors of length 3 in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the j -invariant of the canonical lifting as a function on the j -invariant of the ordinary elliptic curve in characteristic p .

How to cite

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Finotti, Luís R. A.. "Computations with Witt vectors of length $3$." Journal de Théorie des Nombres de Bordeaux 23.2 (2011): 417-454. <http://eudml.org/doc/219820>.

@article{Finotti2011,
abstract = {In this paper we describe how to perform computations with Witt vectors of length $3$ in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the $j$-invariant of the canonical lifting as a function on the $j$-invariant of the ordinary elliptic curve in characteristic $p$.},
affiliation = {Department of Mathematics University of Tennessee Knoxville, TN 37996, USA},
author = {Finotti, Luís R. A.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Witt vectors; elliptic curves; canonical lifting; pseudo-canonical lifting; modular polynomial},
language = {eng},
month = {6},
number = {2},
pages = {417-454},
publisher = {Société Arithmétique de Bordeaux},
title = {Computations with Witt vectors of length $3$},
url = {http://eudml.org/doc/219820},
volume = {23},
year = {2011},
}

TY - JOUR
AU - Finotti, Luís R. A.
TI - Computations with Witt vectors of length $3$
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/6//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 2
SP - 417
EP - 454
AB - In this paper we describe how to perform computations with Witt vectors of length $3$ in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the $j$-invariant of the canonical lifting as a function on the $j$-invariant of the ordinary elliptic curve in characteristic $p$.
LA - eng
KW - Witt vectors; elliptic curves; canonical lifting; pseudo-canonical lifting; modular polynomial
UR - http://eudml.org/doc/219820
ER -

References

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