Fermat’s Last Theorem

@inproceedings{Darmon1995FermatsLT,
  title={Fermat’s Last Theorem},
  author={Henri Darmon and Fred Diamond and Richard Taylor},
  year={1995}
}
The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this paper. They are also grateful to A. Agboola, M. Bertolini, B. Edixhoven, J. Fearnley, R. Gross, L. Guo, F. Jarvis, H. Kisilevsky, E. Liverance, J. Manoharmayum, K. Ribet, D. Rohrlich, M. Rosen, R. Schoof, J.-P. Serre, C. Skinner, D. Thakur, J. Tilouine, J. Tunnell, A. Van der Poorten, and L. Washington for their helpful comments. Darmon thanks… Expand
THE COHOMOLOGY OF SHIMURA VARIETIES AND THE LANGLANDS CORRESPONDENCE
These are greatly extended notes based on talks the author has given surrounding his recent work in [BMY] with A. Bertoloni Meli. This note is certainly very rough and that should be kept in mindExpand
On Generalizing the Pythagorean Theorem
Everyone could understand it; no one could prove it. Posed by the great amateur mathematician, Pierre de Fermat (1601-1665), as a marginal note in his copy of Diophantus' Arithmetica, the problemExpand
Modular Forms and Fermat's Last Theorem
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used byExpand
Modularity of Certain Potentially Barsotti-Tate Galois Representations
where is the reduction of p. These results were subject to hypotheses on the local behavior of p at X, i.e., the restriction of p to a decomposition group at X, and to irreducibility hypotheses onExpand
Lattices in the cohomology of Shimura curves
We prove the main conjectures of Breuil (J Reine Angew Math, 2012) (including a generalisation from the principal series to the cuspidal case) and Dembélé (J Reine Angew Math, 2012), subject to aExpand
Book review for “ Fermat ’ s Last Theorem ” by Takeshi Saito
I was excited to hear that Takeshi Saito’s books on the proof of Fermat’s Last Theorem had been translated and appeared as two fairly thin books in the series “Translation of Mathematical Monographs”Expand
Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory
Let E/Q be an elliptic curve of conductor N and let K be an imaginary quadratic field. Under a certain Heegner hypothesis, Kolyvagin constructed cohomology classes for E using K-CM points andExpand
A fourteenth lecture on Fermat’s Last Theorem∗
The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’sExpand
The Number Theory Revival
After the work of Diophantus, number theory in Europe languished for about 1000 years. In Asia there was significant progress, as we saw in Chapter 5, on topics such as Pell’s equation. The firstExpand
Is There a "Simple" Proof of Fermat's Last Theorem?
We present several approaches to a possible “simple” proof of Fermat’s Last Theorem (FLT), which states that for all n greater than 2, there do not exist x, y, z such that x n + y n = z n , where x,Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 80 REFERENCES
Modular Forms and Fermat's Last Theorem
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used byExpand
Ring-Theoretic Properties of Certain Hecke Algebras
The purpose of this article is to provide a key ingredient of [W2] by establishing that certain minimal Hecke algebras considered there are complete intersections. As is recorded in [W2], a methodExpand
On the method of Coleman and Chabauty
Let C be a curve of genus g >_ 2, defined over a number field K , and let J be the Jacobian of C. Coleman [C2], following Chabauty, has shown how to obtain good bounds on the cardinality of C(K) ifExpand
Algebraic Number Theory
This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessaryExpand
13 lectures on Fermat's last theorem
Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 OtherExpand
Rational isogenies of prime degree
In this table, g is the genus of Xo(N), and v the number of noncuspidal rational points of Xo(N) (which is, in effect, the number of rational N-isogenies classified up to "twist"). For an excellentExpand
Algorithms for Modular Elliptic Curves
This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation. It is in three parts. First, the author describes inExpand
BASE CHANGE FOR GL(2)
R. Langlands shows, in analogy with Artin's original treatment of one-dimensional p, that at least for tetrahedral p, L(s, p) is equal to the L-function L(s, ?) attached to a cuspdidal automorphicExpand
Two-dimensional representations in the arithmetic of modular curves
In the theory of automorphic representations of a reductive algebraic group G over a number field K, it is broadly — but not always — true that irreducible representations occurring in L(GA/GK) occurExpand
History of the Theory of Numbers
THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H.Expand
...
1
2
3
4
5
...