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Research talks;Algebra;Number Theory

Rational points on smooth projective curves of genus $g \ge 2$ over number fields are in finite number thanks to a theorem of Faltings from 1983. The same result was known over function fields of positive characteristic since 1966 thanks to a theorem of Samuel. The aim of the talk is to give a bound as uniform as possible on this number for curves defined over such fields. In a first part we will report on a result by Rémond concerning the number field case and on a way to strengthen it assuming a height conjecture. During the second part we will focus on function fields of positive characteristic and describe a new result obtained in a joined work with Pacheco. Rational points on smooth projective curves of genus $g \ge 2$ over number fields are in finite number thanks to a theorem of Faltings from 1983. The same result was known over function fields of positive characteristic since 1966 thanks to a theorem of Samuel. The aim of the talk is to give a bound as uniform as possible on this number for curves defined over such fields. In a first part we will report on a result by Rémond concerning the ...

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Documents 14G05 | enregistrements trouvés : 70

Bounds for the number of rational points on curves over global fields Pazuki, Fabien | CIRM Nouveau

Interactions of analytic number theory and geometry - lecture 1 Schindler, Damaris | CIRM H Nouveau

Unirational varieties - Part 1 Mella, Massimiliano | CIRM H Nouveau

Algebraic groups: structure ans actions.2015 Clifford lectures on algebraic groups: structure and actionsNew Orleans # March 2-5, 2015 Can, Mahir Bilen | American Mathematical Society 2017 Nouveau

Algorithmic arithmetic, geometry, and coding theory.14th International Conference on arithmetic, geometry, cryptography and coding theoryMarseille # June 3-7, 2013 Ballet, Stéphane ; Perret, Marc ; Zaytsev, Alexey | American Mathematical Society 2015 Nouveau

Algorithms in algebraic geometrybased on the workshopMinneapolis # september 18-22, 2006 Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J. | Springer 2008 Nouveau

Analytic number theory :lectures given at the C.I.M.E. summer school held in Cetraro#July 11-18 Friedlander, J. B. ; Heath-Brown, D. R. ; Iwaniec, Henryk ; Kaczorowski, J. | Springer 2006 Nouveau

Arithmetic geometry.Lectures given at the C.I.M.E. summer schoolCetraro # september 10-15, 2007 Corvaja, Pietro ; Gasbarri, Carlo ; Colliot-Thélène, Jean-Louis ; Swinnerton-Dyer , Peter ; Vojta, Paul | Springer;Fondazione CIME 2011 Nouveau

Arithmetic of higher-dimensional algebriac varieties :proceedings on rational and integral points on higher-dimensional varieties held the American Institute of Mathematics#Dec. 11-20 Poonen, Bjorn ; Tschinkel, Yuri | Birkhäuser 2004 Nouveau

Arithmetic, geometry and coding theory (AGCT 2003) Aubry, Yves ; Lachaud, Gilles | Société Mathématique de France 2005 Nouveau

Arithmetics, geometry, and coding theory (AGCT 2005)Marseille # september 26-30, 2005 Rodier, François ; Vladut, Serge | Société Mathématique de France 2010 Nouveau

Birational geometry, rational curves, and arithmetic.Based on the symposium 'Geometry over closed fields'St. John # february 2012 Bogomolov, Fedor ; Hassett, Brendan ; Tschinkel, Yuri | Springer 2013 Nouveau

Computational arithmetic geometry:AMS special sessionSan Francisco # april 29-30, 2006 Lauter, Kristin E. ; Ribet, Kenneth A. | American Mathematical Society 2008 Nouveau

Diophantine approximation and Abelian varietiesintroductory lecturesheld in Soesterberg, the Netherlands, April 12-16 1992 Edixhoven, B. ; Evertse, J. H. | Springer-Verlag 1993 Nouveau

Diophantine approximation and Abelian varietiesthe instructional conference for Ph. D-students "Diophantine approximation and abelian varieties" from April12- 16, 1992 was held in Soesterberg,The Netherlands Edixhoven, B. ; Evertse, J. H. | Springer-Verlag 1993 Nouveau

Geometric methods in algebra and number theory :conference on ...#Dec. Bogomolov, Fedor ; Tschinkel, Yuri | Birkhäuser 2005 Nouveau

Groupe de Brauer :séminaire tenu à les plans-sur-bex#Mars 16-22 Kervaire, M. ; Ojanguren, M. | Springer-Verlag 1981 Nouveau

Journées arithmétiques de Bordeaux :Mai 27 - Juin 1 | Société Mathématique de France 1975 Nouveau

Ponto racionais em curvas sobre corpos finitos24-28 Julho Garcia, Arnaldo | IMPA 1995 Nouveau

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Algebraic groups: structure ans actions.
2015 Clifford lectures on algebraic groups: structure and actions
New Orleans # March 2-5, 2015 Can, Mahir Bilen | American Mathematical Society 2017 Nouveau

Algorithmic arithmetic, geometry, and coding theory.
14th International Conference on arithmetic, geometry, cryptography and coding theory
Marseille # June 3-7, 2013 Ballet, Stéphane ; Perret, Marc ; Zaytsev, Alexey | American Mathematical Society 2015 Nouveau

Algorithms in algebraic geometry
based on the workshop
Minneapolis # september 18-22, 2006 Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J. | Springer 2008 Nouveau

Analytic number theory :
lectures given at the C.I.M.E. summer school held in Cetraro#July 11-18 Friedlander, J. B. ; Heath-Brown, D. R. ; Iwaniec, Henryk ; Kaczorowski, J. | Springer 2006 Nouveau

Arithmetic geometry.
Lectures given at the C.I.M.E. summer school
Cetraro # september 10-15, 2007 Corvaja, Pietro ; Gasbarri, Carlo ; Colliot-Thélène, Jean-Louis ; Swinnerton-Dyer , Peter ; Vojta, Paul | Springer;Fondazione CIME 2011 Nouveau

Arithmetic of higher-dimensional algebriac varieties :
proceedings on rational and integral points on higher-dimensional varieties held the American Institute of Mathematics#Dec. 11-20 Poonen, Bjorn ; Tschinkel, Yuri | Birkhäuser 2004 Nouveau

Arithmetics, geometry, and coding theory (AGCT 2005)
Marseille # september 26-30, 2005 Rodier, François ; Vladut, Serge | Société Mathématique de France 2010 Nouveau

Birational geometry, rational curves, and arithmetic.
Based on the symposium 'Geometry over closed fields'
St. John # february 2012 Bogomolov, Fedor ; Hassett, Brendan ; Tschinkel, Yuri | Springer 2013 Nouveau

Computational arithmetic geometry:
AMS special session
San Francisco # april 29-30, 2006 Lauter, Kristin E. ; Ribet, Kenneth A. | American Mathematical Society 2008 Nouveau

Diophantine approximation and Abelian varieties
introductory lectures
held in Soesterberg, the Netherlands, April 12-16 1992 Edixhoven, B. ; Evertse, J. H. | Springer-Verlag 1993 Nouveau

Diophantine approximation and Abelian varieties
the instructional conference for Ph. D-students "Diophantine approximation and abelian varieties" from April12- 16, 1992 was held in Soesterberg,The Netherlands Edixhoven, B. ; Evertse, J. H. | Springer-Verlag 1993 Nouveau

Geometric methods in algebra and number theory :
conference on ...#Dec. Bogomolov, Fedor ; Tschinkel, Yuri | Birkhäuser 2005 Nouveau

Groupe de Brauer :
séminaire tenu à les plans-sur-bex#Mars 16-22 Kervaire, M. ; Ojanguren, M. | Springer-Verlag 1981 Nouveau

Journées arithmétiques de Bordeaux :
Mai 27 - Juin 1 | Société Mathématique de France 1975 Nouveau

Ponto racionais em curvas sobre corpos finitos
24-28 Julho Garcia, Arnaldo | IMPA 1995 Nouveau