TN - Teoria de Nombres
http://hdl.handle.net/2117/3728
Fri, 20 Oct 2017 19:55:42 GMT2017-10-20T19:55:42ZConstraints on the automorphism group of a curve
http://hdl.handle.net/2117/108769
Constraints on the automorphism group of a curve
González Rovira, Josep
For a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the non-existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.
Tue, 17 Oct 2017 15:07:55 GMThttp://hdl.handle.net/2117/1087692017-10-17T15:07:55ZGonzález Rovira, JosepFor a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the non-existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.Automorphism group of split Cartan modular curves
http://hdl.handle.net/2117/102154
Automorphism group of split Cartan modular curves
González Rovira, Josep
Wed, 08 Mar 2017 17:43:30 GMThttp://hdl.handle.net/2117/1021542017-03-08T17:43:30ZGonzález Rovira, JosepFunctions and differentials on the non-split Cartan modular curve of level 11
http://hdl.handle.net/2117/101523
Functions and differentials on the non-split Cartan modular curve of level 11
Fernández González, Julio; González Rovira, Josep
The genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11
admits a model defined over Q. We compute generators for its function field in terms of
Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new
part of the Jacobian of the classical modular curve X0(121)
Fri, 24 Feb 2017 10:48:02 GMThttp://hdl.handle.net/2117/1015232017-02-24T10:48:02ZFernández González, JulioGonzález Rovira, JosepThe genus 4 modular curve Xns(11) attached to a non-split Cartan group of level 11
admits a model defined over Q. We compute generators for its function field in terms of
Siegel modular functions. We also show that its Jacobian is isomorphic over Q to the new
part of the Jacobian of the classical modular curve X0(121)30 anys del Seminari de Teoria de Nombres de Barcelona, STNB 2016
http://hdl.handle.net/2117/101086
30 anys del Seminari de Teoria de Nombres de Barcelona, STNB 2016
Alsina Aubach, Montserrat
Wed, 15 Feb 2017 14:07:17 GMThttp://hdl.handle.net/2117/1010862017-02-15T14:07:17ZAlsina Aubach, MontserratEl projecte 7demates
http://hdl.handle.net/2117/101034
El projecte 7demates
Alsina Aubach, Montserrat
Tue, 14 Feb 2017 16:57:47 GMThttp://hdl.handle.net/2117/1010342017-02-14T16:57:47ZAlsina Aubach, MontserratInduced Hopf Galois structures
http://hdl.handle.net/2117/99988
Induced Hopf Galois structures
Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Mª Montserrat
For a ¿nite Galois extension K/k and an intermediate ¿eld F such that Gal(K/F)has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois structures on K/F and F/k.
Wed, 25 Jan 2017 08:51:12 GMThttp://hdl.handle.net/2117/999882017-01-25T08:51:12ZCrespo Vicente, TeresaRío Doval, AnaVela del Olmo, Mª MontserratFor a ¿nite Galois extension K/k and an intermediate ¿eld F such that Gal(K/F)has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois structures on K/F and F/k.Entrevista a Nuno Freitas, Premio José Luis Rubio de Francia 2014
http://hdl.handle.net/2117/86577
Entrevista a Nuno Freitas, Premio José Luis Rubio de Francia 2014
Alsina Aubach, Montserrat
Wed, 04 May 2016 14:09:14 GMThttp://hdl.handle.net/2117/865772016-05-04T14:09:14ZAlsina Aubach, MontserratAutomorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes
http://hdl.handle.net/2117/86360
Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes
Molina Blanco, Santiago; Rotger Cerdà, Víctor
The aim of this short note is to show how the interplay of the action of the automorphism
group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction
and its sets of Heegner points, can be exploited to prove some instances of a conjecture that predicts that any
automorphism must be an Atkin-Lehner involution.
Thu, 28 Apr 2016 11:11:59 GMThttp://hdl.handle.net/2117/863602016-04-28T11:11:59ZMolina Blanco, SantiagoRotger Cerdà, VíctorThe aim of this short note is to show how the interplay of the action of the automorphism
group of a Shimura curve on the special fiber of its Cerednik-Drinfeld’s integral model at a prime of bad reduction
and its sets of Heegner points, can be exploited to prove some instances of a conjecture that predicts that any
automorphism must be an Atkin-Lehner involution.The kernel of Ribet’s isogeny for genus three Shimura curves
http://hdl.handle.net/2117/86355
The kernel of Ribet’s isogeny for genus three Shimura curves
Molina Blanco, Santiago; González Rovira, Josep
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.
Thu, 28 Apr 2016 10:52:55 GMThttp://hdl.handle.net/2117/863552016-04-28T10:52:55ZMolina Blanco, SantiagoGonzález Rovira, JosepThere are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.Fuchsian codes with arbitrarily high code rates
http://hdl.handle.net/2117/84742
Fuchsian codes with arbitrarily high code rates
Blanco Chacón, Iván; Hollanti, Camilla; Alsina Aubach, Montserrat; Remón Adell, Dionís
Recently, Fuchsian codes have been proposed in Blanco-Chacon et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1; e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use.
Fri, 18 Mar 2016 16:57:26 GMThttp://hdl.handle.net/2117/847422016-03-18T16:57:26ZBlanco Chacón, IvánHollanti, CamillaAlsina Aubach, MontserratRemón Adell, DionísRecently, Fuchsian codes have been proposed in Blanco-Chacon et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1; e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use.