In mathematics, the Mordell–Weil theorem states that for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A (...

abelian group. (This is Mordell's Theorem, later generalized to the Mordell–Weil theorem.) Moreover, Mazur's torsion theorem restricts the structure of...

{\displaystyle A(K)} is the Mordell–Weil grouppg 207. The main structure theorem about this group is the Mordell–Weil theorem which shows this group is...

leading to the Mordell–Weil theorem (1928, and shortly applied in Siegel's theorem on integral points). Mordell's theorem had an ad hoc proof; Weil began the...

saying "There's old Stickelberger's result!" Mordell–Weil group Cassels, J. W. S. (1973). "Louis Joel Mordell 1888-1972". Biographical Memoirs of Fellows...

More precisely the Mordell–Weil theorem states that the group E(Q) is a finitely generated (abelian) group. By the fundamental theorem of finitely generated...

who published it in 1935, and Élisabeth Lutz (1937). Mordell–Weil theorem See, for example, Theorem VIII.7.1 of Joseph H. Silverman (1986), "The arithmetic...

the Mordell conjecture and Manin–Mumford conjecture in an abelian variety or semiabelian variety. Mordell–Weil theorem The Mordell–Weil theorem is a...

ISBN 3-540-61223-8. Zbl 0869.11051. J. P. Serre, Lectures on The Mordell-Weil Theorem, Vieweg, 1989. M. D. Fried and M. Jarden, Field Arithmetic, Springer-Verlag...

theorems in Diophantine geometry that are of fundamental importance include: Mordell–Weil theorem Roth's theorem Siegel's theorem Faltings's theorem Serge...

Freeman L (22 May 2005). "Fermat's Last Theorem: Proof for n = 3". Retrieved 23 May 2009. Ribenboim, pp. 24–25 Mordell 1921, pp. 6–8 Edwards 1996, pp. 39–40...

theorem Weil's explicit formula Hasse-Weil bound Hasse–Weil zeta function, and the related Hasse–Weil L-function Mordell–Weil group Mordell–Weil theorem Oka–Weil...

abelian varieties Addition theorem for spherical harmonics Mordell–Weil theorem "Addition theorems in the theory of special functions", Encyclopedia of Mathematics...

the Mordell conjecture, demonstrating that a curve of genus greater than 1 has only finitely many rational points (where the Mordell–Weil theorem only...

d'enfant and the buckyball. Serre, Jean-Pierre (1997). Lectures on the Mordell-Weil theorem. Aspects of Mathematics. Vol. 15. Translated from the French by Martin...

the theorem unconditionally by combining a version of the Thue–Siegel–Roth theorem, from diophantine approximation, with the Mordell–Weil theorem from...

{\sqrt {|D|}}{\log |D|}}.} Theorem (Deuring; 1933)—If the RH is false then h(D) > 1 if |D| is sufficiently large. Theorem (Mordell; 1934)—If the RH is false...

Modularity theorem (number theory) Mordell–Weil theorem (number theory) Multiplicity-one theorem (group representations) Nagell–Lutz theorem (elliptic...

doi:10.1090/noti937. Serre, Jean-Pierre (1997). Lectures on the Mordell-Weil Theorem. Aspects of Mathematics. Vol. 15. Wiesbaden: Vieweg+Teubner Verlag...

Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational numbers or more generally a number field K. Mordell's theorem...

ISBN 978-3-642-39839-1. Serre, Jean-Pierre (1997). Lectures on the Mordell-Weil Theorem. Aspects of Mathematics. Vol. 15. Wiesbaden: Vieweg+Teubner Verlag...

Siegel's theorem on integral points and solution of the S-unit equation. Height functions were crucial to the proofs of the Mordell–Weil theorem and Faltings's...

program modularity theorem Pythagorean triple Pell's equation Elliptic curve Nagell–Lutz theorem Mordell–Weil theorem Mazur's torsion theorem Congruent number...

become identified with descents in the tradition of Fermat. The Mordell–Weil theorem was at the start of what later became a very extensive theory. The...

sequence is finite and effectively computable. This implies the weak Mordell–Weil theorem that its subgroup B(K)/f(A(K)) is finite. There is a notorious problem...

average rank of the Mordell–Weil group of an elliptic curve over Q is bounded above by 7/6. Combining this with the p-parity theorem of Nekovář (2009) and...

for a global field k is finitely generated by the Mordell-Weil theorem. Hence, by the structure theorem for finitely generated abelian groups, it is isomorphic...

B_{\text{max}}(d)=129(5^{d}-1)(3d)^{6}} we get from the structure result behind the Mordell-Weil theorem, i.e. there are two integers n 1 , n 2 {\displaystyle n_{1},n_{2}}...

curves. Numerous direct calculations were done, and the proof of the Mordell–Weil theorem had to proceed by some surrogate of a finiteness proof for a particular...

such as Siegel's theorem on integral points, come from the theory of diophantine approximation. The basic result, the Mordell–Weil theorem in Diophantine...