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:
“Never stay up on the barren heights of cleverness, but come down into the green valleys of silliness.”
—Ludwig Wittgenstein (1889–1951)
“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)