The ubiquity of stability in algebraic geometry

Gerd Faltings (Princeton University, Princeton, New Jersey 08540, U.S.A. & Max-Planck-Institut, Bonn, Germany)

Mumford's notion of stability has found applciations in severl fields, among them moduli-spaces, diophantine approximation and $p$-adic Galois-representations. The purpose of this lecture is to explain how they come up, and to show a little lemma from linear algebra (the tensor-product theorem).