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Abstract: Let p be prime and Zpn the degree n unramified extension of the ring ofp-adic integers Zp. In this paper we give an overview of some very fastalgorithms for common operations in Zpn modulo p^N. Combining existing methodswith recent work of Kedlaya and Umans about modular composition of polynomials,we achieve quasi-linear time algorithms in the parameters n and N, andquasi-linear or quasi-quadratic time in log p, for most basic operations onthese fields, including Galois conjugation, Teichmuller lifting and computingminimal polynomials.



Autor: Hendrik Hubrechts

Fuente: https://arxiv.org/



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