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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.…
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…
Irreducible components of rigid spaces
- B. Conrad
- Mathematics
- 1999
© Annales de l’institut Fourier, 1999, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions…
Modularity of Certain Potentially Barsotti-Tate Galois Representations
- B. Conrad, Fred Diamond, Richard 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…
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…
ARITHMETIC MODULI OF GENERALIZED ELLIPTIC CURVES
- B. Conrad
- MathematicsJournal of the Institute of Mathematics of…
- 11 July 2006
The theory of generalized elliptic curves gives a moduli-theoretic compactification for modular curves when the level is a unit on the base, and the theory of Drinfeld structures on elliptic curves…
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…
DELIGNE’S NOTES ON NAGATA COMPACTIFICATIONS
- B. Conrad
- Mathematics
- 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…
Chow's K/k-image and K/k-trace, and the Lang-Neron theorem
- B. Conrad
- Mathematics
- 2006
Let K/k be an extension of fields, and assume that it is primary: the algebraic closure of k in K is purely inseparable over k. The most interesting case in practice is when K/k is a regular…
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