Citation | Gerd Faltings is a towering figure in mathematics over the last 35 years. His 1983 proof of the Mordell conjecture, the Shafarevich conjecture and the Tate conjecture is perhaps the most beautiful and important paper in number theory in over 100 years. He has made many other fundamental breakthroughs in arithmetic algebraic geometry. These include his proof the Weil-Lang conjecture on rational points on subvarieties of abelian varieties; his proof of the comparison theorem for crystalline and p-adic etale cohomology; his solution of the Gross-Hopkins conjecture; and his construction, with Chai, of integral toroidal compactifications of Siegel varieties. |