Journal Article10.2307/2118559
Modular elliptic curves and Fermat’s Last Theorem
TL;DR: Wiles as discussed by the authors proved that all semistable elliptic curves over the set of rational numbers are modular and showed that Fermat's Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.
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Abstract: When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n > 2 such that an + bn = cn. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.
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Citations
On a relation between modular functions and Dirichlet series: found in the estate of Adolf Hurwitz
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Improved lower bounds for possible solutions in the Second Case of the Fermat Last Theorem and in the Catalan Equation
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An analogy between representations of knot groups and Galois groups
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References
Ring-Theoretic Properties of Certain Hecke Algebras
Richard Taylor,Andrew Wiles +1 more
TL;DR: In this paper, the authors provide a key ingredient of [W2] by establishing that certain minimal Hecke algebras considered there are complete intersections, which is the case for the complete intersection property.
1.2K
L-Functions and Tamagawa Numbers of Motives
Spencer Bloch,Kazuya Kato +1 more
- 01 Jan 2007
TL;DR: In this paper, the authors formulate a conjecture on the values at integer points of L-functions associated to motives and show that it is compatible with isogeny, and include strong results due to one of us (Kato) for elliptic curves with complex multiplication.
771
Class fields of abelian extensions of Q.
Barry Mazur,Andrew Wiles +1 more
TL;DR: In this article, a study of abelian varieties which are good quotients of Jz (N) is presented, where the kernel of the Eisenstein ideal is considered.
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