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)
“This monument, so imposing and tasteful, fittingly typifies the grand and symmetrical character of him in whose honor it has been builded. His was “the arduous greatness of things done.” No friendly hands constructed and placed for his ambition a ladder upon which he might climb. His own brave hands framed and nailed the cleats upon which he climbed to the heights of public usefulness and fame.”
—Benjamin Harrison (1833–1901)
“Never stay up on the barren heights of cleverness, but come down into the green valleys of silliness.”
—Ludwig Wittgenstein (1889–1951)