How many rational points does an algebraic curve have?
October 23, 2013
3:00pm PGH 646
Abstract
A theorem of Faltings ensures that an algebraic curve
defined by equations with rational coefficients have finitely
many rational points provided its genus is at least two. How many
are these finitely many? Can this this number grow, for fixed
genus, by varying the curve? How about the typical curve, how many
points does it have? These are open questions but there has been
some recent progress in understanding them, which I will discuss.
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Last modified: April 11 2016 - 18:14:43