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:
“The heights of popularity and patriotism are still the beaten road to power and tyranny; flattery to treachery; standing armies to arbitrary government; and the glory of God to the temporal interest of the clergy.”
—David Hume (1711–1776)
“We shall make mistakes, but they must never be mistakes which result from faintness of heart or abandonment of moral principles. I remember that my old school master Dr. Peabody said in days that seemed to us then to be secure and untroubled, he said things in life will not always run smoothly, sometimes we will be rising toward the heights and all will seem to reverse itself and start downward. The great thing to remember is that the trend of civilization itself is forever upward.”
—Franklin D. Roosevelt (1882–1945)
“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)