The local Laplace transform of an elementary irregular meromorphic connection
Hien, Marco ; Sabbah, Claude
Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015), p. 133-196 / Harvested from Numdam
Access to full text
Publié le : 2015-01-01
@article{RSMUP_2015__134__133_0,
     author = {Hien, Marco and Sabbah, Claude},
     title = {The local Laplace transform of an elementary irregular meromorphic connection},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {134},
     year = {2015},
     pages = {133-196},
     mrnumber = {3428417},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2015__134__133_0}
}

Hien, Marco; Sabbah, Claude. The local Laplace transform of an elementary irregular meromorphic connection. Rendiconti del Seminario Matematico della Università di Padova, Tome 134 (2015) pp. 133-196. http://gdmltest.u-ga.fr/item/RSMUP_2015__134__133_0/

[BH61] A. Borel and A. Haefliger, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France 89 (1961), 461–513. MR 0149503 (26 #6990) | Numdam | MR 149503 | Zbl 0102.38502

[BJL79] W. Balser, W.B. Jurkat and D.A. Lutz, Birkhoff invariants and Stokes’ multipliers for meromorphic linear differential equations, J. Math. Anal. Appl. 71 (1979), no. 1, 48–94. MR 545861 (81f:34010) | MR 545861 | Zbl 0415.34008

[BM60] A. Borel and J. C. Moore, Homology theory for locally compact spaces, Michigan Math. J. 7 (1960), 137–159. MR 0131271 (24 #A1123) | MR 131271 | Zbl 0116.40301

[Bre97] G. E. Bredon, Sheaf theory, 2nd ed., Graduate Texts in Math., vol. 170, Springer-Verlag, New York, 1997. MR 1481706 (98g:55005) | MR 1481706 | Zbl 0874.55001

[BV89] D.G. Babbitt and V.S. Varadarajan, Local moduli for meromorphic differential equations, Astérisque, vol. 169-170, Société Mathématique de France, Paris, 1989. | MR 1014083 | Zbl 0683.34003

[Del07] P. Deligne, Lettre à B. Malgrange du 22/8/1977, Singularités irrégulières, Correspondance et documents, Documents mathématiques, vol. 5, Société Mathématique de France, Paris, 2007, pp. 21–23. | MR 2387754

[DK13] A. D’Agnolo and M. Kashiwara, Riemann-Hilbert correspondence for holonomic D-modules, Publ. Math. Inst. Hautes Études Sci. (2015), 1–129, arXiv:1311.2374.

[Fan09] Jiangxue Fang, Calculation of local Fourier transforms for formal connections, Sci. China Ser. A 52 (2009), no. 10, 2195–2206, arXiv:0707.0090 MR 2550278 (2010i:14033) | MR 2550278 | Zbl 1195.14023

[HL73] H. Hamm and Lê D.T., Un théorème de Zariski du type de Lefschetz, Ann. Sci. École Norm. Sup. (4) 6 (1973), 317–366. | Numdam | MR 401755 | Zbl 0276.14003

[HS11] C. Hertling and C. Sabbah, Examples of non-commutative Hodge structures, Journal de l’Institut mathématique de Jussieu 10 (2011), no. 3, 635–674, arXiv:0912.2754. | MR 2806464 | Zbl 1246.14019

[Ked10] K. Kedlaya, Good formal structures for flat meromorphic connections, I: surfaces, Duke Math. J. 154 (2010), no. 2, 343–418, arXiv:0811.0190. MR 2682186 | MR 2682186 | Zbl 1204.14010

[KS14] M. Kashiwara and P. Schapira, Irregular holonomic kernels and Laplace transform, Selecta Math. (N.S.) (2015), 1–55, arXiv:1402.3642. | MR 3437833

[Maj84] H. Majima, Asymptotic analysis for integrable connections with irregular singular points, Lect. Notes in Math., vol. 1075, Springer-Verlag, 1984. | MR 757897 | Zbl 0546.58003

[Mal83] B. Malgrange, La classification des connexions irrégulières à une variable, Séminaire E.N.S. Mathématique et Physique (L. Boutet de Monvel, A. Douady, and J.-L. Verdier, eds.), Progress in Math., vol. 37, Birkhäuser, Basel, Boston, 1983, pp. 381–399. | MR 728430 | Zbl 0531.58015

[Mal91] B. Malgrange, Équations différentielles à coefficients polynomiaux, Progress in Math., vol. 96, Birkhäuser, Basel, Boston, 1991. | MR 1117227 | Zbl 0764.32001

[Moc09a] T. Mochizuki, Good formal structure for meromorphic flat connections on smooth projective surfaces, Algebraic Analysis and Around, Advanced Studies in Pure Math., vol. 54, Math. Soc. Japan, Tokyo, 2009, pp. 223–253, arXiv:0803.1346. | MR 2499558 | Zbl 1183.14027

[Moc09b] T. Mochizuki, On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles, Ann. Inst. Fourier (Grenoble) 59 (2009), no. 7, 2819–2837. | Numdam | MR 2649340 | Zbl 1202.32008

[Moc10] T. Mochizuki, Note on the Stokes structure of the Fourier transform, Acta Math. Vietnam. 35 (2010), no. 1, 101–158. | MR 2642166 | Zbl 1201.32016

[Moc11] T. Mochizuki, Wild harmonic bundles and wild pure twistor D -modules, Astérisque, vol. 340, Société Mathématique de France, Paris, 2011. | MR 2919903 | Zbl 1245.32001

[Moc14] T. Mochizuki, Holonomic 𝒟 -modules with Betti structure, Mém. Soc. Math. France (N.S.), vol. 138–139, Société Mathématique de France, 2014, arXiv:1001.2336. | Numdam | MR 3306892 | Zbl 06387011

[Sab93] C. Sabbah, Équations différentielles à points singuliers irréguliers en dimension 2 , Ann. Inst. Fourier (Grenoble) 43 (1993), 1619–1688. | Numdam | MR 1275212 | Zbl 0803.32005

[Sab00] C. Sabbah, Équations différentielles à points singuliers irréguliers et phénomène de Stokes en dimension 2 , Astérisque, vol. 263, Société Mathématique de France, Paris, 2000. | Zbl 0947.32005

[Sab06] C. Sabbah, Monodromy at infinity and Fourier transform II, Publ. RIMS, Kyoto Univ. 42 (2006), 803–835. | MR 2266998 | Zbl 1259.14008

[Sab08] C. Sabbah, An explicit stationary phase formula for the local formal Fourier-Laplace transform, Singularities, vol. 1, Contemp. Math., American Mathematical Society, Providence, RI, 2008, pp. 300–330, arXiv:0706.3570. | MR 2454354 | Zbl 1162.32018

[Sab13a] C. Sabbah, Introduction to Stokes structures, Lect. Notes in Math., vol. 2060, Springer-Verlag, 2013, http://dx.doi.org/10.1007/978-3-642-31695-1 & arXiv:0912.2762 . | MR 2978128 | Zbl 1260.34002

[Sab13b] C. Sabbah, Differential systems of pure Gaussian type, arXiv:1311.4132, 2013.