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- Influence
On the modularity of elliptic curves over Q
- C. Breuil, B. Conrad, Fred Diamond, R. Taylor
- Mathematics
- 15 May 2001
In this paper, building on work of Wiles [Wi] and of Wiles and one of us (R.T.) [TW], we will prove the following two theorems (see §2.2). Theorem A. If E/Q is an elliptic curve, then E is modular.… Expand
Pseudo-reductive Groups
Preface to the second edition Introduction Terminology, conventions, and notation Part I. Constructions, Examples, and Structure Theory: 1. Overview of pseudo-reductivity 2. Root groups and root… Expand
Modularity of Certain Potentially Barsotti-Tate Galois Representations
- B. Conrad, Fred Diamond, R. Taylor
- 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… Expand
Irreducible components of rigid spaces
- B. Conrad
- Mathematics
- 1999
Cet article donne les fondements de la théorie globale des composantes irréductibles d’espaces analytiques rigides sur un corps complet k. Nous prouvons l’excellence d’anneaux locaux sur les espaces… Expand
Complex Multiplication and Lifting Problems
Introduction Algebraic theory of complex multiplication CM lifting over a discrete valuation ring CM lifting of $p$-divisible groups CM lifting of abelian varieties up to isogeny Some arithmetic… Expand
ARITHMETIC MODULI OF GENERALIZED ELLIPTIC CURVES
- B. Conrad
- Mathematics
- 1 April 2007
1.1. Motivation. In [DR], Deligne and Rapoport developed the theory of generalized elliptic curves over arbitrary schemes and they proved that various moduli stacks for (ample) “level-N” structures… Expand
HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES
- B. Conrad
- Mathematics
- 2006
1.1. Motivation. Let E be an elliptic curve over a p-adic integer ring R, and assume that E has supersingular reduction. Consider the 2-dimensional Fp-vector space of characteristic-0 geometric… Expand
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Relative ampleness in rigid geometry
- B. Conrad
- Mathematics
- 2006
Nous developpons une theorie analytique rigide de l'amplitude relative pour les fibres en droites et notons quelques applications a la descente fidelement plate de morphismes et d'objets geometriques… Expand
Several approaches to non-archimedean geometry
- B. Conrad
- Mathematics
- 2008
and it rests upon versions of the inverse and implicit function theorems that can be proved for convergent power series over k by adapting the traditional proofs over R and C. Serre's Harvard… Expand
DELIGNE’S NOTES ON NAGATA COMPACTIFICATIONS
- B. Conrad
- 2009
We provide a proof of Nagata’s compactification theorem: any separated map of finite type between quasi-compact and quasi-separated schemes (e.g., noetherian schemes) factors as an open immersion… Expand
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- 4
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