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Serre’s modularity conjecture (II)
, 2007
"... We provide proofs of Theorems 4.1 and 5.1 of [30]. ..."
On the birational padic section conjecture
"... Abstract. In this manuscript we introduce/prove a Z/p metaabelian form of the birational padic Section Conjecture for curves. This is a much stronger result than the usual padic birational Section Conjecture for curves, and makes an effective padic Section Conjecture for curves quite plausible ..."
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Abstract. In this manuscript we introduce/prove a Z/p metaabelian form of the birational padic Section Conjecture for curves. This is a much stronger result than the usual padic birational Section Conjecture for curves, and makes an effective padic Section Conjecture for curves quite plausible. 1.
On Shafarevich–Tate groups and the arithmetic of Fermat curves
"... Let Q denote the field of rational numbers and Q a fixed algebraic closure of Q. For a fixed prime p such that p ≥ 5, choose a primitive pth root of unity ζ in Q and let K = Q(ζ). If a, b and c are integers such that 0 < a, b, a + b < p and a + b + c = 0, let Fa,b,c denote a smooth projective ..."
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Let Q denote the field of rational numbers and Q a fixed algebraic closure of Q. For a fixed prime p such that p ≥ 5, choose a primitive pth root of unity ζ in Q and let K = Q(ζ). If a, b and c are integers such that 0 < a, b, a + b < p and a + b + c = 0, let Fa,b,c denote a smooth projective model of the affine
A WEAK CHEVALLEYWARNING THEOREM FOR
, 802
"... Abstract. There exists a function f: N → N such that for every positive integer d, every quasifinite field K and every projective hypersurface X of degree d and dimension ≥ f(d), the set X(K) is nonempty. This is a special case of a more general result about intersections of hypersurfaces of fixed ..."
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Abstract. There exists a function f: N → N such that for every positive integer d, every quasifinite field K and every projective hypersurface X of degree d and dimension ≥ f(d), the set X(K) is nonempty. This is a special case of a more general result about intersections of hypersurfaces of fixed degree in projective spaces of sufficiently high dimension over fields with finitely generated Galois groups. 1.