Vojta's conjecture is a conjecture introduced by Paul Vojta (1987) about heights of points on algebraic varieties over number fields. The conjecture was...

Mordell conjecture (already proven in general by Gerd Faltings). As equivalent, Vojta's conjecture in dimension 1. The Erdős–Woods conjecture allowing...

Vojta at the Mathematics Genealogy Project List of Fellows of the American Mathematical Society, retrieved 2013-08-29. Vojta's home page Paul Vojta's...

geometric conjectures such as Szpiro's conjecture on elliptic curves and Vojta's conjecture for curves. The first step is to translate arithmetic information...

Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle? Vojta's conjecture on heights...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

modular varieties. Paul Vojta gave a proof based on Diophantine approximation. Enrico Bombieri found a more elementary variant of Vojta's proof. Brian Lawrence...

involved in the Mordell–Lang conjecture. Vojta conjecture The Vojta conjecture is a complex of conjectures by Paul Vojta, making analogies between Diophantine...

geometry. These include the strong Szpiro conjecture, the hyperbolic Vojta conjecture and the abc conjecture over every number field. In September 2018...

research in the classical one-dimensional theory still continues. Vojta's conjecture H. Weyl (1943). Meromorphic functions and analytic curves. Princeton...

rational points on algebraic varieties, such as the Manin conjecture and Vojta's conjecture, have far-reaching implications for problems in Diophantine...

Gauss–Manin connection may give some important hints for Vojta's conjecture, ABC conjecture and so on; in 2012, he published his Inter-universal Teichmuller...

number theory, the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers...

valued field A valued field is a field with a valuation on it. Vojta Vojta's conjecture Wilson's theorem Wilson's theorem states that n > 1 is prime if...

surfaces gives explicit values for the coefficients of the so-called Lang-Vojta conjecture relating the degree of a curve on a surface with its geometric genus...

pp. 175–191. doi:10.1007/BF02392563 with U. Zannier: Some cases of Vojta's conjecture on integral points over function fields, Journal of Algebraic Geometry...

Extending methods of Paul Vojta, he proved the Mordell–Lang conjecture, which is a generalization of the Mordell conjecture. Together with Gisbert Wüstholz...

topology. In an elementary fashion, he proved the generalized Schoenflies conjecture (his complete proof required an additional result by Marston Morse), around...

equations. These turned out to involve some close parallels and to lead to fresh points of view on the Mordell conjecture and related questions. v t e...

{\displaystyle p} and q {\displaystyle q} . Roth's proof of this fact resolved a conjecture by Siegel. It follows that every irrational algebraic number α satisfies...

175–191. doi:10.1007/BF02392563 with P. Corvaja: "Some cases of Vojta's conjecture on integral points over function fields." Journal of Algebraic Geometry...

this context. Arakelov theory was used by Paul Vojta (1991) to give a new proof of the Mordell conjecture, and by Gerd Faltings (1991) in his proof of Serge...

degrees 1 and 2 (conic sections) occurs in Chapter 17, as does Mordell's conjecture. Siegel's theorem on integral points occurs in Chapter 28. Mordell's theorem...

whose integer solutions are sought Euler's sum of powers conjecture – Disproved conjecture in number theory Generalized taxicab number – Smallest number...

in specific mathematical fields. Grigori Perelman proved the Poincaré conjecture (one of the seven Millennium Prize Problems), and Yuri Matiyasevich gave...

by Paul Vojta to give a new proof of the Mordell conjecture and by Gerd Faltings in his proof of Lang's generalization of the Mordell conjecture. S. J....

optimal, SIAM Journal on Control, 15(?):52–83, 1976 On Kailath's innovation conjecture, Bell System Technical Journal 55:7, pp. 981–1001, 1976 Nonexistence of...

Iwasawa Theory Paul Vojta for his work on Diophantine problems 1997 Andrew J. Wiles for his work on the Shimura–Taniyama conjecture and Fermat's Last Theorem...

on the solutions of the tameness, virtual Haken, and virtual fibering conjectures" James P. Allison – professor at UC Berkeley (1985–2004); 2014 Breakthrough...

Vojta proved in 1999 that a positive answer to Büchi's Problem would follow from a positive answer to a weak version of the Bombieri–Lang conjecture....