The Qth-power algorithm in characteristic 0

2013/01/25 by Leonard, Douglas A.
#13B22 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.6104

Abstract

The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of P:=F[x_n,...,x₁], a polyonomial ring over the finite field F:=Z_q of q elements. Here it is shown how to use this for several small primes q to reconstruct similar integral closures over the rationals Q using the Chinese remainder theorem to piece together presentations in different positive characteristics, and the extended Euclidean algorithm to reconstruct rational fractions to lift these to presentations over Q.

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