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Linear Differential Operators for Polynomial Equations

✍ Scribed by Olivier Cormier; Michael F. Singer; Barry M. Trager; Felix Ulmer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
574 KB
Volume
34
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

Given a squarefree polynomial P ∈ k 0 [x, y], k 0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is absolutely irreducible), the absolute factorization of P over the algebraic closure of k 0 , and calculate information concerning the Galois group of P over k 0 (x) as well as over k 0 (x).

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