Université de Versailles-St Quentin, Laboratoire de Mathématiques, 45 avenue des États-Unis 78035 Versailles cedex, France
e-mail: divizio[at]math.cnrs.fr          Office: bâtiment Fermat, office 3305

Preprints

(with Charlotte Hardouin) "Intrinsic approach to Galois theory of q-difference equations", with a preface to Part V by Anne Granier. 105 pages. (New version of ArXiv:1002.4839. This article also contains the results of the unpublished preprints ArXiv:1205.1696, 1205.1694, 1205.1692.)

 

Edition

(with Tanguy Rivoal) "Arithmetic and Galois theories of differential equations". Séminaires et Congrès 23 (2011).

 

Publications

16. (with Moulay A. Barkatou, Thomas Cluzeau, Jacques-Arthur Weil) "Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System". Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC), 63–70. 
15. (with Charlotte Hardouin and Michael Wibmer) "Difference algebraic relations among solutions of linear differential equations". 61 pages. Journal of the Institute of Mathematics of Jussieu, 16 (2017), No. 1, pp. 59-119. ArXiv:1310.1289.
14. (with Charlotte Hardouin and Michael Wibmer) "Difference Galois theory of linear differential equations". Advances in Mathematics, 260 (2014), Pages 1--58. ArXiv:1302.7198.
13. "Approche galoisienne de la transcendance différentielle", 20 pages. Journée annuelle 2012 de la SMF. ArXiv:1404.3611
12. (with Charlotte Hardouin) "Descent for differential Galois theory of difference equations. Confluence and q-dependency". Pacific Journal of Mathematics, Vol. 256 (2012), No. 1, 79--104. ArXiv:1103.5067.
11. (with Jacques Sauloy) "Outils pour la classification locale des équations aux q-différences linéaires complexes". Séminaires et Congrès 23 (2011), 229-282.  
10. (with Charlotte Hardouin) "Courbures, groupes de Galois génériques et D-groupoïdes de Galois d'un système aux D-différences". C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 951--954..
9. "Local analytic classification of q-difference equations with |q|=1". Journal of Noncommutative Geometry, 3(1), 2009, 125--149. ArXiv:0802.4223
8. (with Changgui Zhang) "On q-summation and confluence". Annales de l'Institut Fourier, 59 no.1 (2009), 347-392. ArXiv: 0709.1610.
7. "An ultrametric version of the Maillet-Malgrange theorem for non linear q-difference equations".
Proceedings of the American Mathematical Society, 136 (2008), 2803-2814. ArXiv: 0709.2464.
6. (with Y. André) "q-difference equations and p-adic local monodromy". Astérisque 296(2004), 55--111.
5. "Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)". "Geometric Aspects of Dwork's Theory", Vol. II, de Gruyter, 615--675. ArXiv: math.NT/0211217.
4. (with J-P. Ramis, J. Sauloy, Ch. Zhang) "Equations aux q-différences". Gazette des mathématiciens, no. 96 (2003), 20--49.
3. "On the arithmetic theory of q-difference equations. The q-analogue of the Grothendieck-Katz's conjecture on p-curvatures". Inventiones Mathematicae 150 (2002) 3, 517--578. DOI: doi:10.1007/s00222-002-0241-z. ArXiv: math.NT/0104178.
List of misprints and errata (pdf file), Another proof of Theorem 6.2.2 (pdf file).
2. "Sur la théorie géométrique des G-fonctions (Le théorème de Chudnovsky à plusieurs variables)".
Mathematische Annalen 319 (2001) 1, 181--213. DOI:10.1007/PL00004428.
1. "On arithmetic size of linear differential equation".
Journal of Algebra 242 (2001) 1, 31--59. DOI: 10.1006/jabr.2000.8750.
  

 

Unpublished preprints

"Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series) ". ArXiv:0902.4169.
(with F. Baldassarri) "Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces". Preprint, 25 pages. ArXiv: 0709.2008. The article by F. Baldassarri "Continuity of the radius of convergence of differential equations on p-adic analytic curves", Invent. Math. 182 (2010), no. 3, 513–584 improves the results of the paper above (which is in several variables) in the case of meromorphic connections on an analytic curve.

 

Other mathematical texts

Mémoire d'habilitation hdr.pdf
Ph.D.THESIS "Étude arithmétique des équations aux q-différences et des équations différentielles"
abstract.pdf, introduction.pdf, partI.pdf , partII.pdf , appendix.pdf.