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18
Fields of moduli of threepoint Gcovers with cyclic pSylow, I.
, 2011
"... We examine in detail the stable reduction of GGalois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic pSylow subgroup of order pn. If G is further assumed to be psolvable (i.e., G has no nonabelian simple composition fac ..."
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We examine in detail the stable reduction of GGalois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic pSylow subgroup of order pn. If G is further assumed to be psolvable (i.e., G has no nonabelian simple composition factors with order divisible by p), we obtain the following consequence: Suppose f: Y → P1 is a threepoint GGalois cover defined over C. Then the nth higher ramification groups above p for the upper numbering for the extension K/Q vanish, where K is the field of moduli of f. This extends work of Beckmann and Wewers. Additionally, we completely describe the stable model of a general
Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic
"... Abstract. Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p> 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits ..."
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Cited by 5 (3 self)
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Abstract. Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p> 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow psubgroup, we prove that N is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of N is a free profinite group of countable cardinality. 1.
The local lifting problem for actions of finite groups on curves. Annales scientifiques de l’ENS
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Equiramified deformations of covers in positive characteristic
"... Suppose φ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of φ in equal characteristic, which are equiramified in that the branch locus is constant and the ramification filtration is fixed. We show tha ..."
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Cited by 4 (0 self)
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Suppose φ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of φ in equal characteristic, which are equiramified in that the branch locus is constant and the ramification filtration is fixed. We show that the moduli space Mφ parametrizing equiramified deformations of φ is a subscheme of an explicitly constructed scheme. This allows us to give an explicit upper and lower bound for the Krull dimension dφ of Mφ. These bounds depend only on the ramification filtration of φ. When φ is an abelian pgroup cover, we use class field theory to show that the upper bound for dφ is realized.
Vanishing cycles and wild monodromy
, 910
"... Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y → P 1 be a threepoint Gcover defined over K, where G has a cyclic pSylow subgroup P. We examine the stable model of f, in particular, the minimal extension K st /K such ..."
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Cited by 3 (2 self)
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Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y → P 1 be a threepoint Gcover defined over K, where G has a cyclic pSylow subgroup P. We examine the stable model of f, in particular, the minimal extension K st /K such that the stable model is defined over K st. Our main result is that, if g(Y) � 2, the ramification indices of f are prime to p, and P  = p n, then the pSylow subgroup of Gal(K st /K) has exponent dividing p n−1. This extends work of Raynaud in the case that P  = p. 1.
Wild cyclicbytame extensions
, 807
"... Suppose G is a semidirect product of the form Z/p n ⋊ Z/m where p is prime and m is relatively prime to p. Suppose K is a complete local field of characteristic p> 0. The main result states necessary and sufficient conditions on the ramification filtrations that occur for wildly ramified GGaloi ..."
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Suppose G is a semidirect product of the form Z/p n ⋊ Z/m where p is prime and m is relatively prime to p. Suppose K is a complete local field of characteristic p> 0. The main result states necessary and sufficient conditions on the ramification filtrations that occur for wildly ramified GGalois extensions of K. In addition, we prove that there exists a parameter space for GGalois extensions of K with given ramification filtration whose dimension depends only on the ramification filtration. We provide explicit equations for wild cyclic extensions of K of degree p 3.