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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 295 - Colloquium
Jack Sonn
Technion, Haifa, Israel
Irreducible polynomials which are reducible locally everywhere
Abstract:
There exists a polynomial $f(x)$ of degree $n$ with integer coefficients which is irreducible over the rationals but reducible modulo $p$ for all primes $p$ if and only if $n$ is not a prime number. The same result holds with "reducible mod $p$" replaced by "reducible over $Q_p$", and generalizes to arbitrary global fields. (Joint work with Bob Guralnick and Murray Schacher)
Host: Adrian Wadsworth
January 13, 2005
3:00 PM
AP&M 6438
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