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Newton polygons of higher order in algebraic number theory

Autor
Guàrdia, J.; Montes, J.; Nart, E.
Tipus d'activitat
Article en revista
Revista
Transactions of the American Mathematical Society
Data de publicació
2012-01-10
Volum
364
Número
1
Pàgina inicial
361
Pàgina final
416
DOI
https://doi.org/10.1090/S0002-9947-2011-05442-5 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/14810 Obrir en finestra nova
Resum
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a p-adic eld, together with relevant arithmetic information about the elds generated by the irreducible factors. This carries out a program suggested by . Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number elds.
Citació
Guardia, J.; Montes, J.; Nart, E. Newton polygons of higher order in algebraic number theory. "Transactions of the American Mathematical Society", 10 Gener 2012, vol. 364, núm. 1, p. 361-416.
Paraules clau
Discriminant, Integral basis, Local field, Newton polygon, Number field, P-adic factorization, Prime ideal decomposition
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

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