On the tangent space of the deformation functor of curves with automorphisms

Kontogeorgis, Aristides

doi:10.2140/ant.2007.1.119

Cited by 10 publications

(10 citation statements)

References 30 publications

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“…Finally, in section 5 we give an application to the computation of the tangent space of the local deformation functor in the sense of J.Bertin and A. Mézard [1]. The results are given in terms of the Boseck invariants, and coincide with computations done previously by other authors [1],[13], [11], [12] using completely different methods. This allows us to verify our complicated computations concerning the Galois module structure.…”

Section: Introductionmentioning

confidence: 64%

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On holomorphic polydifferentials in positive characteristic

Karanikolopoulos

2012

Mathematische Nachrichten

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ABSTRACT. In this paper we study the space Ω(m), of holomorphic m-(poly)differentials of a function field of a curve defined over an algebraically closed field of characteristic p > 0 when G is cyclic or elementary abelian group of order p n ; we give bases for each case when the base field is rational, introduce the Boseck invariants and give an elementary approach to the G module structure of Ω(m) in terms of Boseck invariants. The last computation is achieved without any restriction on the base field in the cyclic case, while in the elementary abelian case it is assumed that the base field is rational. An application to the computation of the tangent space of the deformation functor of curves with automorphisms is given.

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Section: Introductionmentioning

confidence: 64%

“…Observe that the restriction for Γ k (m), given in Eq. (12), when the genus of E was zero, is the same restriction that results from our basis in order to ensure that an m-(poly)differential is holomorphic (see Eq. (21)).…”

Section: Remark 11mentioning

confidence: 99%

On holomorphic polydifferentials in positive characteristic

Karanikolopoulos

2012

Mathematische Nachrichten

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“…In this case, we also describe the corresponding space of parameters and, when n = 2, we give necessary and sufficient conditions on the parameters for two curves of the family to be isomorphic and we characterize the subfamily corresponding to the special curves that are studied in Section 6.1.1. In each case, we eventually try to determine the different nonisomorphic models which can occur for the corresponding group G. Following what has been done for the p-cyclic case in [Ro08c,§2.10], one should compare the results obtained in this section with the works of Pries [Pr05] and Kontogeorgis [Kon07].…”

Section: A Universal Familymentioning

confidence: 94%

Large p-group actions with a p-elementary abelian derived group

Rocher

2009

Journal of Algebra

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Let k be an algebraically closed field of characteristic p > 0 and C a connected nonsingular projective curve over k with genus g 2.Let (C, G) be a "big action," i.e. a pairp−1 . The aim of this paper is to describe the big actions whose derived group G is p-elementary abelian. In particular, we obtain a structure theorem for the functions parametrizing the ArtinSchreier cover C → C /G . Using Artin-Schreier duality, we shift to a group-theoretic point of view to characterize relevant cases. Then, we display universal families and discuss the corresponding deformation space for p = 5.

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“…Following [Bertin and Mézard 2000], in the case where G is cyclic of order p, Pries [2005] and Kontogeorgis [2007] have obtained lower and upper bounds for the dimension of the tangent space, with explicit computations in some special cases, in particular when G is an abelian p-group. (See also [Cornelissen and Kato 2003]).…”

Section: Introductionmentioning

confidence: 99%

Smooth curves having a large automorphismp-group in characteristicp >0

Matignon

Rocher

2008

ANT

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Let k be an algebraically closed field of characteristic p > 0 and C a connected nonsingular projective curve over k with genus g ≥ 2. This paper continues our study of big actions, that is, pairs (C, G) where G is a p-subgroup of the k-automorphism group of C such that |G|/g > 2 p/( p−1). If G 2 denotes the second ramification group of G at the unique ramification point of the cover C → C/G, we display necessary conditions on G 2 for (C, G) to be a big action, which allows us to pursue the classification of big actions.Our main source of examples comes from the construction of curves with many rational points using ray class field theory for global function fields, as initiated by J.-P. Serre and continued by Lauter and by Auer. In particular, we obtain explicit examples of big actions with G 2 abelian of large exponent.

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On the tangent space of the deformation functor of curves with automorphisms

Cited by 10 publications

References 30 publications

On holomorphic polydifferentials in positive characteristic

On holomorphic polydifferentials in positive characteristic

Large p-group actions with a p-elementary abelian derived group

Smooth curves having a large automorphismp-group in characteristicp >0

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