Heights
There is a canonical Néron–Tate height function, which is a quadratic form; it has some remarkable properties, amongst all height functions designed to pick of finite sets in A(K) of points of height (roughly, logarithmic size of co-ordinates) at most h.
Read more about this topic: Arithmetic Of Abelian Varieties
Famous quotes containing the word heights:
“Men go out to admire the heights of mountains, the huge waves of the sea, the broadest spans of rivers, the circle of ocean, the revolutions of stars, and leave themselves behind.”
—St. Augustine (354–430)
“Give me the keys. I feel for the common chord again,
Sliding by semi-tones till I sink to a minor,—yes,
And I blunt it into a ninth, and I stand on alien ground,
Surveying a while the heights I rolled from into the deep;
Which, hark, I have dared and done, for my resting-place is found,
The C Major of this life: so, now I will try to sleep.”
—Robert Browning (1812–1889)
“Forgetting: that is a divine capacity. And whoever aspires to the heights and wants to fly must cast off much that is heavy and make himself light—I call it a divine capacity for lightness.”
—Friedrich Nietzsche (1844–1900)