منابع مشابه
Superficial Fibres of Generic Projections
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Let P (x, y) be a rational polynomial. If the curve (P (x, y) = k), k ∈ Q, is irreducible and admits an infinite number of points whose coordinates are integers, Siegel’s theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar-MohSuzuki theorem, that there exists an algebraic automorphism sending P (x, y) to the poly...
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Fix ρ : GQ,S → GL2(k) absolutely irreducible, and let ρ : GQ,S → GL2(R) be the universal deformation. We’re interested in the map R → Tm for some Hecke algebra defined in terms of ρ. Note that the Hecke algebra is 1-dimensional, and even finite free over Zp. The universal deformation ring R, however, often has dimension > 1 and nonzero p-torsion. In other words, the surjection R ։ Tm is not eve...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2010
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x09004503