|Hilbert's Tenth Problem over Q and its subrings|
Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients would decide whether there exists a solution in integers. In 1970, Matijasevic, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous problem with Z replaced by Q is still unknown, and there is not even agreement among experts as to what the answer should be. Attempts to prove a negative answer have come into conflict with conjectures of Mazur on the ``topology of rational points.''
|Web page: Alexandru I. Suciu||Comments to: email@example.com|
|Posted: March 30, 2003||URL: http://www.math.neu.edu/bhmn/poonen.html|