SMF

Théories de Galois et arithmétique des équations différentielles

Arithmetic and Galois theories of differential equations

Di Vizio, Lucia, Rivoal, Tanguy
  • Année : 2011
  • Tome : 23
  • Format : Papier
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 33C70, 12H05, 14K15, 11G10, 12G05, 33C60, 11F52, 11J93, 34M15, 11D88, 34M03,34M35, 39A13, 12H10, 18D10, 39A, 11S80, 14J32 11S80, 11J99, 14J32, 12H25, 12H10, 12H20, 12H99, 11S15; 11S20, 39A10, 33E20, 33E05
  • Nb. de pages : XVIII + 405
  • ISBN : 978-285629-331-7
  • ISSN : 1285-2783
Ce volume constitue les actes de l'école d'été Théories galoisiennes et arithmétiques des équations différentielles qui s'est tenue au CIRM, Luminy, du 21 au 25 septembre 2009. Cette école a réuni des mathématiciens de sensibilités diverses autour du thème des équations différentielles ordinaires, avec une attention particulière portée à l'arithmétique. Il est composé de cinq textes de survols, correspondant aux cinq cours donnés lors de l'école, ainsi que de six articles originaux écrits par certains des orateurs des exposés donnés en complément des cours. De plus, ce volume contient une relecture, par B. Chiarellotto, G. Gerotto et F. J. Sullivan, des notes d'un cours sur les modules exponentiels donné par B. M. Dwork à l'université de Padoue en 1994.
This volume contains the proceedings of the summer school Galoisian and Arithmetic Theory of Differential Equations, held at the CIRM, in Luminy, from September 21st to September 25th 2009. This school brought together mathematicians from various areas of research united by their interest in ordinary differential equations, particularly those that arise in arithmetic. It consists of five surveys, corresponding to the five lecture courses given during the school, plus six original papers, corresponding to research talks also given on this occasion. The volume also contains a reworking, by B. Chiarellotto, G. Gerotto et F. J. Sullivan, of notes of the lectures on exponential modules given by B. M. Dwork at the university of Padova in 1994.
Differential Galois Theories, Linear and non-linear differential Galois theory, Abelian Varieties, Galois cohomology, Kummer theory, A-hypergeometric function, Appell function, Horn function, Euler integral, Dwork module, Multiplicity estimate, Drinfeld modular form, Drinfeld quasi-modular form, $A$-modular form, $A$-quasi-modular form, Pseudogroups,Differential Invariants, Ultrametric, irregularity, index, radius of convergence, Exponential Module, $G$-function, $q$-difference equations, formal ification, analytic ification, Newton polygon ; slope filtration ; small divisors, Tannakian categories, Unipotent radical, Galois groups, $t$-motives, Calabi–Yau manifolds, integrality of mirror maps, $p$-adic analysis, harmonic numbers, hypergeometric differential équations, integrality of mirror maps, $p$-adic analysis, Dwork's theory in several variables, harmonic numbers, hypergeometric differential équations, $p$-adic $q$-difference equations, $p$-adic differential equations, Confluence, Deformation, unipotent, $p-$adic local monodromy theorem, roots of unity, Berkovich spaces, stratifications, radius of convergence, Finite difference systems, difference Galois theory, Elliptic hypergeometric functions, elliptic gamma functions, elliptic beta integrals
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