Special Colloquium
Kirsten Eisentraeger
University of Michigan
Hilbert's Tenth Problem for algebraic function fields
Abstract: Hilbert's Tenth Problem in its original form was to find an algorithm
to decide, given a polynomial equation f(x_1,....,x_n)=0 with
integer coefficients, whether it has a solution with x_1, ..., x_n
integers.
Matiyasevich proved that no such algorithm exists, i.e. Hilbert's
Tenth Problem is undecidable. Since then, analogues of this problem
have been studied by asking the same question for polynomial equations
with coefficients and solutions in other commutative rings.
In this talk we will discuss how elliptic curves of rank one can be
used to prove undecidability of Hilbert's Tenth Problem for algebraic
function fields, such as function fields over p-adic fields and
function fields of varieties over the complex numbers of dimension at least
two.
Friday January 26, 2007 at 3:00 PM in SEO 636