Algorithms for enumerating invariants and extensions of local fields

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Brian Sinclair (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Sebastian Pauli

Abstract: There are many computationally difficult problems in the study of p-adic fields, among them the classification of field extensions and the decomposition of global ideals. The main goal of this work is present efficient algorithms, leveraging the Newton polygons and residual polynomials, to solve many of these problems faster and more efficiently than present methods. Considering additional invariants, we extend Krasner's mass formula, dramatically improve general extension enumeration using the reduced Eisenstein polynomials of Monge, and provide a detailed account of algorithms that compute Okutsu invariants, which have many uses, through the lens of partitioning the set of zeros of polynomials.

Additional Information

Language: English
Date: 2015
Algorithms, Local class field theory, Number theory, P-adic fields
Class field theory
p-adic fields
Number theory

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