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Modularity of certain potentially Barsotti-Tate Galois representations |
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| Authors: | Brian Conrad Fred Diamond Richard Taylor |
| Institution: | Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 ; Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854 ; Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 |
| Abstract: | We show that certain potentially semistable lifts of modular mod representations are themselves modular. As a result we show that any elliptic curve over the rational numbers with conductor not divisible by 27 is modular. |
| Keywords: | Hecke algebra Galois representation modular curves |
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