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RISS 인기검색어
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- 저자 : Savitt, David Lawrence (검색결과 1 건)
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Modularity of some potentially Barsotti-Tate Galois representations
Savitt, David Lawrence Harvard University 2001 해외박사(DDOD)
소속기관이 구독 중이 아닌 경우 오후 4시부터 익일 오전 9시까지 원문보기가 가능합니다.
We prove a portion of a conjecture of Conrad-Diamond-Taylor, which yields proofs of some 2-dimensional cases of the Fontaine-Mazur conjectures. Let <math> <f> <g>r</g></f> </math> be a continuous odd irreducible <italic>l</italic>-adic Galois representation (<italic>l</italic> an odd prime) satisfying the hypotheses of the Fontaine-Mazur conjecture and such that <math> <f> <ovl><g>r</g></ovl></f> </math> is modular. The notable additional hypotheses we must impose in order to conclude that <math> <f> <g>r</g></f> </math> is modular are that <math> <f> <g>r</g></f> </math> is potentially Barsotti-Tate, that the Weil-Deligne representation associated to <math> <f> <g>r</g></f> </math> is irreducible and tamely ramified, and that <math> <f> <ovl><g>r</g></ovl></f> </math> is conjugate to a representation over <bold>F</bold><italic><sub> l</sub></italic> which is reducible with scalar centralizer. The proof follows techniques of Breuil, Conrad, Diamond, and Taylor, and in particular requires extensive calculation with Breuil's classification of <italic>l</italic>-torsion finite flat group schemes over base schemes with high ramification.
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