Abstract
The calculation of the discriminant is at the very core of techniques of algebraic number theory. It is involved in basis problems (Chapter 9), ramified primes (Chapter 10), and, now, in the computation of the conductor \( \tilde f \) associated with an abelian extension K/k. Two of the most startling yet simple techniques of algebraic number theory can be motivated by their use in facilitating the computation of discriminants, namely the theory of forms (associated with Kronecker) and local number theory (associated with Hensel).
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© 1978 Springer-Verlag New York Inc.
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Cohn, H. (1978). Discriminant and Conductor. In: A Classical Invitation to Algebraic Numbers and Class Fields. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9950-9_17
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DOI: https://doi.org/10.1007/978-1-4612-9950-9_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90345-3
Online ISBN: 978-1-4612-9950-9
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