13,605 research outputs found
Polynomials with prescribed bad primes
We tabulate polynomials in Z[t] with a given factorization partition, bad
reduction entirely within a given set of primes, and satisfying auxiliary
conditions associated to 0, 1, and infinity. We explain how these sets of
polynomials are of particular interest because of their role in the
construction of nonsolvable number fields of arbitrarily large degree and
bounded ramification. Finally we discuss the similar but technically more
complicated tabulation problem corresponding to removing the auxiliary
conditions.Comment: 26 pages, 3 figure
Hurwitz Monodromy and Full Number Fields
We give conditions for the monodromy group of a Hurwitz space over the
configuration space of branch points to be the full alternating or symmetric
group on the degree. Specializing the resulting coverings suggests the
existence of many number fields with full Galois group and surprisingly little
ramification --- for example, the existence of infinitely many such number
fields unramified away from {2,3,5}
A database of number fields
We describe an online database of number fields which accompanies this paper
The database centers on complete lists of number fields with prescribed
invariants. Our description here focuses on summarizing tables and connections
to theoretical issues of current interest.Comment: 25 pages, 1 figur
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