Abstract |
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Let K be an
algebraic function field of characteristic 2 with constant
field CK. Let C be
the algebraic closure of a finite field in
K. Assume that C has an extension of degree 2. Assume that
there are elements u,x of
K with u transcendental over CK and
x algebraic over C(u) and such that
K = CK(u,x). Then
Hilbert’s Tenth Problem over K
is undecidable. Together with Shlapentokh’s result for odd
characteristic this implies that Hilbert’s Tenth Problem
for any such field K of
finite characteristic is undecidable. In particular,
Hilbert’s Tenth Problem for any algebraic function
field with finite constant field is
undecidable.
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Authors
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Berkeley, California.