Pure Maths Colloquium: The theory of heights
22 November 2010 17:15 in CM221
he height of a variety measures the amount of information needed to
represent the variety.
It is the arithmetic analogue of the degree in geometry. Classically,
there are two kinds of applications of the theory of heights. On the
one hand, bounds on the height lead to finiteness results. The
prototypical example being Falting's proof of Mordell's conjecture.
On the other hand, exact values of the height can be related with
special values of L-functions. For instance, Gross-Zagier computation
of the height of special cycles on a modular curve, is a key
ingredient in the proof of Birch and Swinnerton-Dyer conjecture for
elliptic curves of rank one. In this talk we will give a survey on the
theory of heights.
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