TN - Teoria de Nombres
http://hdl.handle.net/2117/3728
2016-05-04T06:22:35ZAutomorphisms 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.
2016-04-28T11:11:59ZMolina 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.
2016-04-28T10:52:55ZMolina 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.
2016-03-18T16:57:26ZBlanco 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.El programa Ciencia en Acción. Entrevista a Rosa M. Ros, directora del programa
http://hdl.handle.net/2117/84664
El programa Ciencia en Acción. Entrevista a Rosa M. Ros, directora del programa
Alsina Aubach, Montserrat
2016-03-17T16:18:41ZAlsina Aubach, MontserratNuno Freitas, premi José Luis Rubio de Francia de la RSME
http://hdl.handle.net/2117/84663
Nuno Freitas, premi José Luis Rubio de Francia de la RSME
Alsina Aubach, Montserrat
2016-03-17T16:08:22ZAlsina Aubach, MontserratPilar Bayer, medalla d'honor 2015 de la Xarxa Vives
http://hdl.handle.net/2117/84659
Pilar Bayer, medalla d'honor 2015 de la Xarxa Vives
Alsina Aubach, Montserrat
2016-03-17T16:01:34ZAlsina Aubach, MontserratFrobenius distribution for quotients of Fermat curves of prime exponent
http://hdl.handle.net/2117/81570
Frobenius distribution for quotients of Fermat curves of prime exponent
Fité, Francesc; González Rovira, Josep; Lario Loyo, Joan Carles
Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as quotients of C by certain subgroups of automorphisms of C. It is well known that Jac(C_k) is the power of an absolutely simple abelian variety B_k with complex multiplication. We call degenerate those pairs (l,k) for which B_k has degenerate CM type. For a non-degenerate pair (l,k), we compute the Sato-Tate group of Jac(C_k), prove the generalized Sato-Tate Conjecture for it, and give an explicit method to compute the moments and measures of the involved distributions. Regardless of (l,k) being degenerate or not, we also obtain Frobenius equidistribution results for primes of certain residue degrees in the l-th cyclotomic field. Key to our results is a detailed study of the rank of certain generalized Demjanenko matrices.
2016-01-15T19:45:28ZFité, FrancescGonzález Rovira, JosepLario Loyo, Joan CarlesLet C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as quotients of C by certain subgroups of automorphisms of C. It is well known that Jac(C_k) is the power of an absolutely simple abelian variety B_k with complex multiplication. We call degenerate those pairs (l,k) for which B_k has degenerate CM type. For a non-degenerate pair (l,k), we compute the Sato-Tate group of Jac(C_k), prove the generalized Sato-Tate Conjecture for it, and give an explicit method to compute the moments and measures of the involved distributions. Regardless of (l,k) being degenerate or not, we also obtain Frobenius equidistribution results for primes of certain residue degrees in the l-th cyclotomic field. Key to our results is a detailed study of the rank of certain generalized Demjanenko matrices.Modular forms with large coefficient fields via congruences
http://hdl.handle.net/2117/81139
Modular forms with large coefficient fields via congruences
Dieulefait, Luis; Jiménez Urroz, Jorge; Ribet, Keneth
We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.
2016-01-08T12:27:07ZDieulefait, LuisJiménez Urroz, JorgeRibet, KenethWe use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.On the Galois correspondence theorem in separable Hopf Galois theory
http://hdl.handle.net/2117/80381
On the Galois correspondence theorem in separable Hopf Galois theory
Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Mª Montserrat
In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.
2015-12-10T11:13:14ZCrespo Vicente, TeresaRío Doval, AnaVela del Olmo, Mª MontserratIn this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.From Galois to Hopf Galois: theory and practice
http://hdl.handle.net/2117/80188
From Galois to Hopf Galois: theory and practice
Crespo Vicente, Teresa; Río Doval, Ana; Vela del Olmo, Mª Montserrat
Hopf Galois theory expands the classical Galois theory by con- sidering the Galois property in terms of the action of the group algebra k [ G ] on K/k and then replacing it by the action of a Hopf algebra. We review the case of separable extensions where the Hopf Galois property admits a group-theoretical formulation suitable for counting and classifying, and also to perform explicit computations and explic it descriptions of all the ingredients involved in a Hopf Galois structure. At the end we give just a glimpse of how this theory is used in the context of Ga lois module theory for wildly ramified extensions
2015-12-04T12:08:29ZCrespo Vicente, TeresaRío Doval, AnaVela del Olmo, Mª MontserratHopf Galois theory expands the classical Galois theory by con- sidering the Galois property in terms of the action of the group algebra k [ G ] on K/k and then replacing it by the action of a Hopf algebra. We review the case of separable extensions where the Hopf Galois property admits a group-theoretical formulation suitable for counting and classifying, and also to perform explicit computations and explic it descriptions of all the ingredients involved in a Hopf Galois structure. At the end we give just a glimpse of how this theory is used in the context of Ga lois module theory for wildly ramified extensions