Proofs
Faltings' original proof used the known reduction to a case of the Tate conjecture, and a number of tools from algebraic geometry, including the theory of Néron models. A very different proof, based on diophantine approximation, was found by Paul Vojta. A more elementary variant of Vojta's proof was given by Enrico Bombieri.
Read more about this topic: Faltings' Theorem
Famous quotes containing the word proofs:
“To invent without scruple a new principle to every new phenomenon, instead of adapting it to the old; to overload our hypothesis with a variety of this kind, are certain proofs that none of these principles is the just one, and that we only desire, by a number of falsehoods, to cover our ignorance of the truth.”
—David Hume (1711–1776)
“Trifles light as air
Are to the jealous confirmation strong
As proofs of holy writ.”
—William Shakespeare (1564–1616)
“I do not think that a Physician should be admitted into the College till he could bring proofs of his having cured, in his own person, at least four incurable distempers.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)