Uniform Sheaves and Differential Equations
Rendiconti del Seminario Matematico della Università di Padova, Volume 128  (2012), p. 345-372
@article{RSMUP_2012__128__345_0,
     author = {Andr\'e, Yves},
     title = {Uniform Sheaves and Differential Equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {128},
     year = {2012},
     pages = {345-372},
     mrnumber = {3076836},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2012__128__345_0}
}
André, Yves. Uniform Sheaves and Differential Equations. Rendiconti del Seminario Matematico della Università di Padova, Volume 128 (2012) , pp. 345-372. http://www.numdam.org/item/RSMUP_2012__128__345_0/

[1] Y. André, Filtrations de Hasse-Arf et monodomie p -adique, Invent. Math. 148 , no. 2 (2002), pp. 285-317. | MR 1906151 | Zbl 1081.12003

[2] Y. André, Galois representations, differential equations and q -difference equations: sketch of a p -adic unification, Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I. Astérisque 296 (2004), pp. 43-53. | MR 2135684 | Zbl 1074.12005

[3] Y. André - F. Baldassarri, De Rham cohomology of differential modules on algebraic varieties, Progress in Mathematics 189. Birkhäuser Verlag, Basel (2001). | MR 1807281 | Zbl 0995.14003

[4] M. Audin, Henri Cartan et André Weil. Du XXe siècle et de la topologie, journées X-UPS 2012, Ecole Polytechnique, to appear.

[5] M. Baker, Uniform structures and Berkovich spaces, unpublished preprint (2006), available at http://people

[6] F. Baldassarri, Differential modules and singular points of p-adic differential equations, Adv. in Math. 44 , no. 2 (1982), pp. 155-179. | MR 658539 | Zbl 0493.12030

[7] F. Baldassarri, Comparaison entre la cohomologie algébrique et la cohomologie p-adique rigide à coefficients dans un module différentiel. I. Cas des courbes, Invent. Math. 87 , no. 1 (1987), pp. 83-99. | MR 862713 | Zbl 0586.14009

[8] F. Baldassarri, Connexions sur les courbes p -adiques: existence d’un modèle “clean”, finitude de la cohomologie et formules de Euler-Poincaré, talk at the Strasbourg conference, 16/4/2012.

[9] F. Baldassarri - B. Chiarellotto, Algebraic versus rigid cohomology with logarithmic coefficients, Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), pp. 11-50, Perspect. Math., 15 , Academic Press, San Diego, CA (1994). | MR 1307391 | Zbl 0833.14010

[10] H. Bentley - H. Herrlich - M. Husek, The historical development of uniform, proximal and nearness concepts in Topology, Handbook of the History of General Topology, Vol. 2, C. Aull and R. Lowen eds., Kluwer, Dordrecht (2001), pp. 577-629. | MR 1795163 | Zbl 0936.54028

[11] V. Berkovich, Non-Archimedean analytic geometry: first steps, p -adic geometry, Univ. Lecture Ser., 45, Amer. Math. Soc., Providence, RI, 2008. | MR 2482344 | Zbl 1153.14019

[12] V. Berkovich, Integration of one-forms on p -adic spaces, Annals of Mathematics Studies, 162 . Princeton University Press (2007). | MR 2263704 | Zbl 1161.14001

[13] P. Berthelot, Cohomologie rigide et cohomologie rigide à supports propres, preprint Rennes (1996).

[14] J. Bochnak - M. Coste - M.-F. Roy, Géométrie algébrique réelle, Ergebnisse der Mathematik, Springer (1987). | MR 949442 | Zbl 0633.14016

[15] S. Bosch - U. Güntzer - R. Remmert, Non-archimedean analysis, Grundlehren der math. Wissenschaften 261 , Springer-Verlag (1984). | MR 746961 | Zbl 0539.14017

[16] N. Bourbaki, Eléments de mathématique. Topologie générale, english translation: Springer (1989). | Zbl 1107.54001

[17] G. Brümmer, Categorical aspects of the theory of quasi-uniform spaces, Rend. Istit. Mat. Univ. Trieste, Suppl. Vol. XXX (1999), pp. 45-74. | MR 1718995 | Zbl 0934.54015

[18] G. Châtelet, L'enchantement du virtuel, C. Alunni and C. Paoletti eds., Editions Rue d'Ulm, Paris (2011).

[19] G. Christol - Z. Mebkhout, Sur le théorème de l’indice des équations différentielles p -adiques IV, Invent. Math. 143 (2001), pp. 629-672. | MR 1817646 | Zbl 1078.12501

[20] R. Crew, F -isocrystals and p -adic representations, in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math. 46 Part 2, Amer. Math. Soc., Providence, RI, 1987, pp. 111-138. | MR 927977 | Zbl 0639.14011

[21] J. Dauns - K. Hofmann, Representations of rings by continuous sections, Memoir Amer. Math. Soc. 83 (1968). | MR 247487 | Zbl 0174.05703

[22] P. Deligne, Equations différentielles à points singuliers réguliers, Lecture notes in math. 163 , Springer (1970). | MR 417174 | Zbl 0244.14004

[23] P. Deligne, Lettre à J.-P. Ramis, 7/1/86, Singularités irrégulières, Correspondances et documents, (P. Deligne, B. Malgrange, J.-P. Ramis), Documents math. 5 , Soc. Math. Fr. (2007). | MR 2387754 | Zbl 1130.14001

[24] L. Di Vizio - J.-P. Ramis - J. Sauloy - C. Zhang, Equations aux q -différences, Gaz. Math. No. 96 (2003), pp. 20-49. | MR 1988639 | Zbl 1063.39015

[25] M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc., 142 (1969), pp. 43-60. | MR 251026 | Zbl 0184.29401

[26] R. Huber, Etale cohomology of rigid analytic varieties and adic spaces, Aspects of Mathematics, E30. Friedr. Vieweg, Braunschweig, 1996. | MR 1734903 | Zbl 0868.14010

[27] R. Huber, Swan representations associated with rigid analytic curves, J. Reine Angew. Math. 537 (2001), pp. 165-234. | MR 1856262 | Zbl 0979.14012

[28] J. Isbell, Uniform spaces, Math. Surveys n 12, A.M.S. Providence (1974). | Zbl 0124.15601

[29] M. Kashiwara - P. Shapira, Ind-sheaves, Astérisque 271 , Soc. Math. Fr. (2001). | MR 1827714 | Zbl 0993.32009

[30] K. Kedlaya, Fourier transforms and p -adic “Weil II”, Compos. Math. 142 , no. 6 (2006), pp. 1426-1450. | MR 2278753 | Zbl 1119.14014

[31] H.-P. Künzi, Nonsymmetric distances and their associated topologies. About the origins of basic ideas in the area of asymmetric topology, Handbook of the History of General Topology, Vol. 3, C. Aull and R. Lowen eds., Kluwer, Dordrecht (2001), pp. 853-968. | MR 1900267 | Zbl 1002.54002

[32] P. Lambrinos, A note on quasi-uniform continuity, Bull. Austral. Math. Soc. 8 (1973), pp. 389-392. | MR 321017 | Zbl 0254.54026

[33] B. Le Stum, The overconvergent site, Mém. Soc. Math. Fr., 127 (2011). | Numdam | MR 2952779 | Zbl 1246.14028

[34] M. Loday-Richaud - G. Pourcin, On index theorems for linear ordinary differential operators, Ann. Inst. Fourier (Grenoble) 47 , no. 5 (1997), pp. 1379-1424. | Numdam | MR 1600379 | Zbl 0901.34012

[35] G. Morando, Tempered solutions of 𝒟 -modules on complex curves and formal invariants, Ann. Inst. Fourier Grenoble 59, 4 (2009), pp. 1611-1630. | Numdam | MR 2566969 | Zbl 1218.32015

[36] M. Murdeshwar - S. Naimpally, Quasi-uniform topological spaces, Nordhoff (1966). | MR 211386 | Zbl 0139.40501

[37] R. Meyer, Bornological versus topological analysis in metrizable spaces, Banach algebras and their applications, 249-278, Contemp. Math. 363, Amer. Math. Soc., Providence, RI (2004). | MR 2097966 | Zbl 1081.46004

[38] S. Naimpally - B. Warrack, Proximity spaces, Cambridge Univ. Press (1970). | MR 278261 | Zbl 1184.54027

[39] L. Ramero, Local monodromy in non-archimedean analytic geometry, Publ. Math. Inst. Hautes É tudes Sci. 102 (2005), pp. 167-280. | Numdam | MR 2217053 | Zbl 1111.14012

[40] J.-P. Ramis, Les derniers travaux de Jean Martinet, Annales de l'institut Fourier, 42 , no. 1-2 (1992), pp. 15-47. | Numdam | MR 1162556 | Zbl 0927.01031

[41] J. Rivera-Letelier, Notes sur la droite projective de Berkovich, preprint (2006). Available at arxiv:abs/math.MG/0605676.

[42] J. Roques, Sur les systèmes aux (q -)différences. Thèse Univ. Toulouse III (2007).

[43] C. Sabbah, De Rham and Dolbeault cohomology of D-modules (Oberwolfach 2007), lecture notes available at http://www.math.polytechnique.fr/cmat/sabbah/livres.html

[44] J. Tukey, Convergence and uniformity in topology, Annals of Mathematics Studies, no. 2. Princeton University Press, Princeton, N. J (1940). | JFM 66.0961.01 | MR 2515

[45] M. Van Der Put - M. Singer, Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, 328 . Springer-Verlag, Berlin, 2003. | MR 1960772 | Zbl 1036.12008

[46] L. Waelbroeck, review of Bornologies and functional analysis by H. Hogbe-Nlend (Math. Studies 26, North-Holland), Bull. Amer. Math. Soc. 84 (1978). | MR 1567102 | Zbl 0359.46004

[47] A. Weil, Sur les espaces à structure uniforme et sur la topologie générale, Publications de l'Institut de mathématiques de l'Université de Strasbourg, Hermann, Paris (1937). | JFM 63.0569.04 | Zbl 0019.18604

[SGA 4] M. Artin - A. Grothendieck - J.-L. Verdier, Théorie des topos et cohomologie étale des schémas, Lecture notes in math. 269 , 270 , 305 , Springer (1972), pp. 13.