Ring-Theoretic Properties of Certain Hecke Algebras
@article{Taylor1995RingTheoreticPO, title={Ring-Theoretic Properties of Certain Hecke Algebras}, author={Richard Taylor and Andrew Wiles}, journal={Annals of Mathematics}, year={1995}, volume={141}, pages={553-572} }
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 method going back to Mazur [M] allows one to show that these algebras are Gorenstein, but for the complete intersection property a new approach is required. The methods of this paper are related to those of Chapter 3 of [W2]. The methods of Section 3 of this paper are based on a previous approach of one of…
1,107 Citations
Deformations of Induced Galois Representations S . Cho
- Mathematics
- 2000
The object of this article is to study the behavior of certain deformation problems and Hecke rings under base change to a real quadratic field. These questions were the subject of conjectures by…
Deformations of induced Galois representations
- Mathematics
- 2003
The object of this article is to study the behavior of certain deformation problems and Hecke rings under base change to a real quadratic field. These questions were the subject of conjectures by…
L-INVARIANTS OF TATE CURVES
- Mathematics
- 2009
In Sections 2 to 4 of this paper we describe a computation expressing the Linvariant of Greenberg in an explicit form for the symmetric n-th power for n ≤ 2 of the Tate module of an elliptic curve…
Modularity of 2-dimensional Galois representations
- Mathematics
- 2005
Our aim is to explain some recent results on modularity of 2-dimensional potentially Barsotti-Tate Galois representations. That such representations should arise from modular forms is a special case…
Modularity of Certain Potentially Barsotti-Tate Galois Representations
- Mathematics
- 1999
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 on…
MODULAR GALOIS REPRESENTATIONS OF "NEBEN" TYPE
- Mathematics
- 2000
In 1995 in [W] Theorem 0.2, A. Wiles proved, under some mild conditions (and relying on a ring theoretic result on Hecke algebras in [TW]), that if a p–adic Galois representation is congruent modulo…
The Taylor-Wiles construction and multiplicity one
- Mathematics
- 1997
Wiles’ proof [17] of the modularity of semistable elliptic curves over Q relies on a construction of Taylor and Wiles [16] showing that certain Hecke algebras are complete intersections. These Hecke…
Wiles defect of Hecke algebras via local-global arguments
- Mathematics
- 2021
In his work on modularity of elliptic curves and Fermat’s Last Theorem, A. Wiles introduced two measures of congruences between Galois representations and between modular forms. One measure is…
L-Invariant of the Symmetric Powers of Tate Curves
- Mathematics
- 2009
In my earlier paper [H07] and in my talk at the workshop on “Arithmetic Algebraic Geometry” at RIMS in September 2006, we made explicit a conjectural formula of the L-invariant of symmetric powers of…
References
SHOWING 1-10 OF 17 REFERENCES
Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?)
- Mathematics
- 1995
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…
On certain Galois representations related to the modular curve $X_1(p)$
- Mathematics
- 1995
© Foundation Compositio Mathematica, 1995, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…
Modular curves and the eisenstein ideal
- Mathematics
- 1977
© Publications mathématiques de l’I.H.É.S., 1977, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
Introduction to commutative algebra and algebraic geometry
- MathematicsActa Applicandae Mathematicae
- 1991
Foreword.- Preface.- Preface to the English Edition.- Terminology.- Algebraic varieties.- Dimension.- Regular and rational functions on algebraic varieties.- The local-global principle in commutative…
On a variation of Mazur's deformation functor
- Mathematics
- 1993
© Foundation Compositio Mathematica, 1993, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…
Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
- Mathematics
- 1986
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1986, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…
Construction de représentations $p$-adiques
- Mathematics
- 1982
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1982, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…