Abstract:Nous montrons que le polygone de Newton d'une équation aux q-différences linéaire ne dépend que du module aux q-différences correspondant. Nous interprétons les classiques résultats de factorisation convergente de Adams-Birkhoff-Guenther en termes d'existence d'une filtration canonique par les pentes. De plus, le gradué associé possède d'excellentes propriétés fonctorielles (d'où son interêt pour la classification) et tensorielles (d'où son interêt pour la théorie de Galois).
“…Guenther, see [Bir], where they present normal forms for these equations. This case is also treated in [R-S-Z, Sau2,Sau3]. (3) Each F i,j has the natural structure of algebraic group over C and is in fact equal to Ext 1 (P i , P j ).…”
Section: Moduli Spaces For Q-difference Equationsmentioning
confidence: 99%
“…Adams, see [Bir]. A modern proof is provided in [Sau3]. The difference module M over K is called split if M is isomorphic to gr(M ) (in other words, M is a direct sum of pure modules).…”
“…Guenther, see [Bir], where they present normal forms for these equations. This case is also treated in [R-S-Z, Sau2,Sau3]. (3) Each F i,j has the natural structure of algebraic group over C and is in fact equal to Ext 1 (P i , P j ).…”
Section: Moduli Spaces For Q-difference Equationsmentioning
confidence: 99%
“…Adams, see [Bir]. A modern proof is provided in [Sau3]. The difference module M over K is called split if M is isomorphic to gr(M ) (in other words, M is a direct sum of pure modules).…”
“…the work of F. Marotte and Ch. Zhang [MZ00], J. Sauloy [Sau04], M. van der Put and M. Reversat [vdPR06], that have their roots in the work of G.D. Birkhoff and P.E. Guether [BG41] and C.R.…”
Section: 2]) There Exists a Natural Bijection Between The Isomorphmentioning
confidence: 99%
“…We recall some generalities on q-difference modules (for a more detailed exposition cf. for instance [DV02, Part I], [Sau04] and [DVRSZ03]). …”
Section: Analytic Classification Of Admissible Q-difference Modulesmentioning
confidence: 99%
“…For other algebraic constructions (tensor product, internal Hom,...) we refer to [DV02] and [Sau04].…”
Section: Analytic Classification Of Admissible Q-difference Modulesmentioning
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