Relevant bibliographies by topics / Stack ramified Galois covers

Academic literature on the topic 'Stack ramified Galois covers'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Stack ramified Galois covers"

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TONINI, FABIO. "RAMIFIED GALOIS COVERS VIA MONOIDAL FUNCTORS." Transformation Groups 22, no. 3 (June 23, 2016): 845–68. http://dx.doi.org/10.1007/s00031-016-9395-4.

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Kontogeorgis, Aristides, and Panagiotis Paramantzoglou. "Galois action on homology of generalized Fermat Curves." Quarterly Journal of Mathematics 71, no. 4 (November 28, 2020): 1377–417. http://dx.doi.org/10.1093/qmath/haaa038.

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Abstract The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups H. We provide a unified study of the action of both cover Galois group H and the absolute Galois group $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on the pro-$\ell$ homology of the curves in study. Also the relation to the pro-$\ell$ Burau representation is investigated.
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Malle, Gunter, and David P. Roberts. "Number Fields with Discriminant ±2a3b and Galois Group An or Sn." LMS Journal of Computation and Mathematics 8 (2005): 80–101. http://dx.doi.org/10.1112/s1461157000000905.

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AbstractThe authors present three-point and four-point covers having bad reduction at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 12, 18, 28, and 33. By specializing these covers, they obtain number fields ramified at 2 and 3 only, with Galois group An or Sn for n equal to 9, 10, 11, 12, 17, 18, 25, 28, 30, and 33.
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Kock, Bernhard. "Galois structure of Zariski cohomology for weakly ramified covers of curves." American Journal of Mathematics 126, no. 5 (2004): 1085–107. http://dx.doi.org/10.1353/ajm.2004.0037.

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Corvaja, Pietro, Julian Lawrence Demeio, Ariyan Javanpeykar, Davide Lombardo, and Umberto Zannier. "On the distribution of rational points on ramified covers of abelian varieties." Compositio Mathematica 158, no. 11 (November 2022): 2109–55. http://dx.doi.org/10.1112/s0010437x22007746.

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We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields $k$ of characteristic zero. For example, given a ramified cover $\pi : X \to A$ , where $A$ is an abelian variety over $k$ with a dense set of $k$ -rational points, we prove that there is a finite-index coset $C \subset A(k)$ such that $\pi (X(k))$ is disjoint from $C$ . Our results do not seem to be in the range of other methods available at present; they confirm predictions coming from Lang's conjectures on rational points, and also go in the direction of an issue raised by Serre regarding possible applications to the inverse Galois problem. Finally, the conclusions of our work may be seen as a sharp version of Hilbert's irreducibility theorem for abelian varieties.
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PARDINI, RITA, and FRANCESCA TOVENA. "ON THE FUNDAMENTAL GROUP OF AN ABELIAN COVER." International Journal of Mathematics 06, no. 05 (October 1995): 767–89. http://dx.doi.org/10.1142/s0129167x9500033x.

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Let X, Y be smooth complex projective varieties of dimension n≥2 and let f: Y→X be a totally ramified abelian cover. Assume that the components of the branch divisor of f are ample. Then the map f*: π1(Y)→π1(X) is surjective and gives rise to a central extension: [Formula: see text] where K is a finite group. Here we show how the kernel K and the cohomology class c(f) ∈ H2(π1(X), K) of (1) can be computed in terms of the Chern classes of the components of the branch divisor of f and of the eigensheaves of [Formula: see text] under the action of the Galois group. Using this result, for any integer m>0, we construct m varieties X1,…, Xm no two of which are homeomorphic, even though they have the same numerical invariants and they are realized as covers of the same projective variety X with the same Galois group, branch locus and inertia subgroups.
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Fischbacher-Weitz, Helena, Bernhard Köck, and Adriano Marmora. "Galois-Module Theory for Wildly Ramified Covers of Curves over Finite Fields (with an Appendix by Bernhard Köck and Adriano Marmora)." Documenta Mathematica 24 (2019): 175–208. http://dx.doi.org/10.4171/dm/678.

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Grosselli, Gian Paolo, and Abolfazl Mohajer. "Shimura subvarieties in the Prym locus of ramified Galois coverings." Collectanea Mathematica, December 20, 2021. http://dx.doi.org/10.1007/s13348-021-00342-5.

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AbstractWe study Shimura (special) subvarieties in the moduli space $$A_{p,D}$$ A p , D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to $${{\mathbb {P}}}^1$$ P 1 . We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.
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Goluboff, J. Ross. "Genus Six Curves, K3 Surfaces, and Stable Pairs." International Mathematics Research Notices, January 15, 2020. http://dx.doi.org/10.1093/imrn/rnz372.

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Abstract A general smooth curve of genus six lies on a quintic del Pezzo surface. Artebani and Kondō [ 4] construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special genus six curves. In this paper, we construct a smooth Deligne–Mumford stack ${\mathfrak{P}}_0$ parametrizing certain stable surface-curve pairs, which essentially resolves this map. Moreover, we give an explicit description of pairs in ${\mathfrak{P}}_0$ containing special curves.
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Dissertations / Theses on the topic "Stack ramified Galois covers"

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Fabio, Tonini. "Stacks of ramified Galois covers." Doctoral thesis, 2013. http://hdl.handle.net/2158/1156898.

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Book chapters on the topic "Stack ramified Galois covers"

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Colombo, Elisabetta, and Paola Frediani. "Second Fundamental Form of the Prym Map in the Ramified Case." In Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants, 55–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51795-3_4.

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