Leírás
Austrian-Hungarian Diophantine Number Theory seminar
Abstract:
In case of genus 2 curves we know by the celebrated result of Faltings that there are only finitely many rational points. The result cannot be used to actually determine the complete set of points in concrete examples. An older result by Chabauty provides a bound on the number of solutions and sometimes the bound is equal to the number of known points. However, this method does not work if the rank of the Mordell-Weil group is larger (>1). In case of integral points one can get a very large upper bound for the solutions via Baker's method. Using this huge bound one has two different approaches to handle the problem. The first one uses the so-called Mordell-Weil sieve, the second one uses hyperelliptic logarithms. Both procedures have been successfully applied to determine the set of integral points in case of genus 2 curves with Mordell-Weil groups of ranks 3,4,5 and 6. If the rank is larger (>4), then the time of the computation is getting longer and longer (couple of hours). In this talk we show that it is possible to combine the two approaches making possible to reduce the running times.
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m06cf015398b65f64abeffcd14956696b