TN - Teoria de Nombres
http://hdl.handle.net/2117/3728
2018-02-21T07:43:34ZOn the Sato-Tate conjecture for non-generic abelian surfaces
http://hdl.handle.net/2117/114198
On the Sato-Tate conjecture for non-generic abelian surfaces
Johansson, Christian; Fite Naya, Francesc
We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fité, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.
2018-02-16T13:27:14ZJohansson, ChristianFite Naya, FrancescWe prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fité, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
http://hdl.handle.net/2117/113813
Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
Darmon, Henri; Rotger Cerdà, Víctor
This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension at most $ 4$. When the associated $ L$-function vanishes (to even order $ \ge 2$) at its central point, two canonical classes in the corresponding Selmer group are constructed and shown to be linearly independent assuming the non-vanishing of a Garrett-Hida $ p$-adic $ L$-function at a point lying outside its range of classical interpolation. The key tool for both results is the study of certain $ p$-adic families of global Galois cohomology classes arising from Gross-Kudla-Schoen diagonal cycles in a tower of triple products of modular curves.
2018-02-06T13:49:38ZDarmon, HenriRotger Cerdà, VíctorThis article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension at most $ 4$. When the associated $ L$-function vanishes (to even order $ \ge 2$) at its central point, two canonical classes in the corresponding Selmer group are constructed and shown to be linearly independent assuming the non-vanishing of a Garrett-Hida $ p$-adic $ L$-function at a point lying outside its range of classical interpolation. The key tool for both results is the study of certain $ p$-adic families of global Galois cohomology classes arising from Gross-Kudla-Schoen diagonal cycles in a tower of triple products of modular curves.Constraints 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.
2017-10-17T15:07:55ZGonzález 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
2017-03-08T17:43:30ZGonzález 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)
2017-02-24T10:48:02ZFernández 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
2017-02-15T14:07:17ZAlsina Aubach, MontserratEl projecte 7demates
http://hdl.handle.net/2117/101034
El projecte 7demates
Alsina Aubach, Montserrat
2017-02-14T16:57:47ZAlsina 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.
2017-01-25T08:51:12ZCrespo 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
2016-05-04T14:09:14ZAlsina 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.
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.