Polarizable twistor ūĚíü-modules
Astérisque, no. 300 (2005) , 214 p.
@book{AST_2005__300__R1_0,
     author = {Sabbah, Claude},
     title = {Polarizable twistor $\mathcal{D}$-modules},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {300},
     year = {2005},
     zbl = {1085.32014},
     language = {en},
     url = {http://www.numdam.org/item/AST_2005__300__R1_0/}
}
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Sabbah, Claude. Polarizable twistor $\mathcal{D}$-modules. Astérisque, no. 300 (2005), 214 p. http://numdam.org/item/AST_2005__300__R1_0/

[1] D. Barlet & H.-M. Maire "Développements asymptotiques. transformation de Mellin complexe et intégration sur les fibres", in Séminaire d'analyse 1985-1986 (P. Lelong. P. Dolbeault & H. Skoda, eds.). Lect. Notes in Math., vol. 1295. Springer-Verlag. 1987. p. 11-23. | Zbl

[2] D. Barlet & H.-M. Maire "Asymptotic expansion of complex integrals via Mellin transform", J. Fund. Anal. 83 (1989). p. 233-257. | DOI | Zbl

[3] A. A. Beilinson. J. N. Bernstein & P. Deligne "Faisceaux pervers", in Analyse et topologie sur les espaces singuliers. Astérisque, vol. 100. Société Mathématique de France. 1982. p. 7-171. | Numdam | Zbl

[4] O. Biquard "Fibr√©s de Higgs et connexions int√©grables: le cas logarithmique (diviseur lisse)". Ann. scient. √Čc. Norm. Sup. 4e s√©rie 30 (1997). p. 41-96. | DOI | Numdam | Zbl | EuDML

[5] O. Biquard & Ph. Boalch "Wild nonabelian Hodge theory on curves", Compositio Math, 140 (2004), p. 179-204. | DOI | Zbl

[6] J.-E. Bj√∂rk Analytic ūĚíü-modules and applications. Kluwer Academic Publisher. Dordrecht. 1993. | Zbl

[7] G. Boeckle & –°. Khare "Mod ‚Ąď representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)". arXiv: math. NT/0312490, 2003. | Zbl

[8] L. Bungart - "On analytic fiber bundles. I: Holomorphic fiber bundles with infinite dimensional fibers". Topology 7 (1968). p. 55-68. | DOI | Zbl

[9] Espaces fibrés et homotopie - Séminaire Henri Cartan (1949/1950). vol. 2. 1956.

[10] F. Castro "Exercices sur le complexe de de Rham et l'image directe des ūĚíü-modules", in √Čl√©ments de la th√©orie des syst√®mes diff√©rentiels [39], p. 15-45. | Zbl

[11] M. A. De Cataldo & L. Migliorini "The Hodge theory of algebraic maps", Ann. scient. √Čc. Norm. Sup. 4e s√©rie (to appear), arXiv: math. AG/0306030. | Numdam | EuDML | Zbl

[12] E. Cattani, A. Kaplan & W. Schmid "L 2 and intersection cohomologies for a polarizable variation of Hodge structure". Invent. Math. 87 (1987), p. 217-252. | DOI | EuDML | Zbl

[13] K. Corlette - "Flat G-bundles with canonical metrics", J. Differential Geom. 28 (1988), p. 361-382. | DOI | Zbl

[14] M. Cornalba & P. A. Griffiths "Analytic cycles and vector bundles on noncompact algebraic varieties". Invent. Math. 28 (1975), p. 1-106. | DOI | EuDML | Zbl

[15] P. Deligne - "Th√©or√®me de Lefschetz et crit√®res de d√©g√©n√©rescence de suites spectrales", Publ. Math. Inst. Hautes √Čtudes Sci. 35 (1968), p. 107-126. | DOI | Numdam | EuDML | Zbl

[16] P. Deligne, √Čquations diff√©rentielles √† points singuliers r√©guliers. Lect. Notes in Math., vol. 163, Springer-Verlag, 1970. | Zbl

[17] P. Deligne, "Th√©orie de Hodge II", Publ. Math. Inst. Hautes √Čtudes Sci. 40 (1971), p. 5-57. | DOI | Numdam | EuDML | Zbl

[18] P. Deligne, "Cohomologie à supports propres(exposé XVII)", in SGA 4. Lect. Notes in Math., vol. 305, Springer-Verlag, 1973, p. 252-480. | Zbl

[19] P. Deligne, "Le formalisme des cycles évanescents (exposés 13 et 14)", in SGA 7 II, Lect. Notes in Math., vol. 340. Springer-Verlag. 1973. p. 82-173. | Zbl

[20] P. Deligne, "La conjecture de Weil. II". Publ. Math. Inst. Hautes √Čtudes Sci. 52 (1980), p. 137-252. | DOI | Numdam | EuDML | Zbl

[21] P. Deligne, "Un théorème de finitude pour la monodromie", in Discrete groups in geometry and, analysis (New Haven. Conn.. 1984). Progress in Math., vol. 67. Birkhäuser, Boston, 1987, p. 1-19. | DOI | Zbl

[22] J.-P. Demailly "Théorie de Hodge L 2 et théorèmes d'annulation", in Introduction à la théorie de Hodge, Panoramas et Synthèses, vol. 3. Société Mathématique de France, 1996, p. 3-111. | Zbl

[23] A. Douai & C. Sabbah "Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)". Ann. Inst. Fourier (Grenoble) 53 (2003). no. 4. p. 1055-1116. | DOI | Numdam | EuDML | Zbl

[24] V. Drinfeld - "On a conjecture of Kashiwara". Math. Res. Lett. 8 (2001). p. 713-728. | DOI | Zbl

[25] O. Gabber "The integrability of the characteristic variety", Amer. J. Math. 103 (1981), p. 445-468. | DOI | Zbl | MR

[26] D. Gaitsgory "On de Jong's conjecture". arXiv: math. AG/0402184, 2004. | Zbl | MR

[27] R. Godement Topologie algébrique et théorie des faisceaux. Hermann. Paris. 1964. | Zbl | MR

[28] F. Guillén & V. Navarro Aznar "Sur le théorème local des cycles invariants". Duke Math. J. 61 (1990), p. 133-155. | DOI | Zbl | MR

[29] H. Hamm & Lê D. T. "Lefschetz theorems on quasi-projective varieties", Bull. Soc. math, France 113 (1985). p. 123-142. | DOI | Numdam | EuDML | Zbl | MR

[30] C. Hertling - "tt * geometry. Frobenius manifolds, their connections, and the construction for singularities", J. reine angew. Math. 555 (2003), p. 77-161. | Zbl | MR

[31] J. Jost & K. Zuo "Harmonic maps and SL(r,‚Ąā)-representations of fundamental groups of quasi-projective manifolds"; J. Algebraic Geometry 5 (1996), p. 77-106. | Zbl | MR

[32] J. Jost & K. Zuo, "Harmonic maps of infinite energy and rigidity results for representations of fundamental groups of quasiprojective varieties". J. Differential Geom. 47 (1997). p. 469-503. | DOI | Zbl | MR

[33] M. Kashiwara "Vanishing cycles sheaves and holonomic systems of differential equations", in Algebraic geometry (Tokyo/Kyoto, 1982), Lect. Notes in Math., vol. 1016. Springer-Verlag, 1983. p. 134-142. | DOI | Zbl | MR

[34] M. Kashiwara. "Semisimple holonomic ūĚíü-modules", in Topological Field Theory, Primitive Forms and Related Topics [36], p. 267-271. | Zbl | MR

[35] M. Kashiwara & T. Kawai "The Poincaré lemma for variations of polarized Hodge structure". Publ. RIMS. Kyoto Univ. 23 (1987), p. 345-407. | DOI | Zbl | MR

[36] M. Kashiwara. K. Saito. A. Matsuo & I. Satake (eds.) - Topological Field Theory, Primitive Forms and Related Topics, Progress in Math., vol. 160, Birkhäuser, Basel. Boston, 1998. | MR

[37] M. Kashiwara & P. Schapira Sheaves on Manifolds, Grundlehren der mathematischen Wissenschaften, vol. 292, Springer-Verlag, 1990. | Zbl | MR

[38] J. Leiterer - "Holomorphic vector bundles and the Oka-Grauert principle", in Several complex variables. IV. Algebraic aspects of complex analysis. Encycl. Math. Sci., vol. 10. Springer-Verlag, 1990, p. 63-103. | Zbl

[39] Ph. Maisonobe & C. Sabbah (eds.) Images directes et constructibilité. Les cours du CIMPA. Travaux en cours, vol. 46, Hermann, Paris. 1993.

[40] B. Malgrange "Polyn√īme de Bernstein-Sato et cohomologie √©vanescente". in Analyse et topologie sur les espaces singuliers [70]. p. 243-267. | Numdam | Zbl | MR

[41] B. Malgrange, "Sur les déformations isomonodromiques, I. II", in Séminaire E.N.S. Mathématique et Physique (L. Boutet de Monvel, A. Douady & J.-L. Verdier, eds.). Progress in Math., vol. 37. Birkhäusen, Basel. Boston, 1983, p. 401-438. | MR | Zbl

[42] B. Malgrange, "Sur les images directes de ūĚíü-modules". Manuscripta Math. 50 (1985). p. 49-71. | DOI | EuDML | Zbl | MR

[43] B. Malgrange, √Čquations diff√©rentielles √† coefficients polynominaux, Progress in Math., vol. 96. Birkh√§user. Basel. Boston. 1991. | Zbl | MR

[44] Z. Mebkhout Le formalisme des six op√©rations de Grothendieck pour les ūĚíü-modules coh√©rents. Travaux en cours, vol. 35. Hermann. Paris. 1989. | Zbl | MR

[45] Z. Mebkhout, "Le th√©or√®me de comparaison entre cohomologies de de Rham d'une vari√©t√© alg√©brique complexe et le th√©or√®me d'existence de Riemann", Publ. Math. Inst. Hautes √Čtudes Sci. 69 (1989). p. 47-89. | DOI | EuDML | Numdam | Zbl | MR

[46] Z. Mebkhout & C. Sabbah "¬ßIII.4 ūĚíü-modules et cycles evanescents", in Le formalisme des six op√©rations de Grothendieck pour les ūĚíü-modules coh√©rents [44], p. 201-239. | MR

[47] T. Mochizuki "Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure", J. Differential Geom. 62 (2002). p. 351-559. | DOI | Zbl | MR

[48] T. Mochizuki, "Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules". arXiv: math. DG/0312230. 2003. | Zbl | MR

[49] T. Mochizuki,"A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric", arXiv: math. DG/0402122. 2004.

[50] B. Opic & A. Kufner Hardy-type inequalities. Pitman Research Notes in Mathematics, vol. 219. Longman Scientific & Technical. Harlow. 1990. | Zbl | MR

[51] C. Sabbah - "ūĚíü-modules et cycles √©vanescents (d'apr√®s B. Malgrange et M. Kashiwara)", in Conf√©rence de La Rabida 1984. vol. III. Hermann, Paris, 1987, p. 53-98. | Zbl | MR

[52] C. Sabbah, "Monodromy at infinity and Fourier transform", Publ. RIMS, Kyoto Univ. 33 (1997). no. 4. p. 643-685. | DOI | Zbl | MR

[53] C. Sabbah, "Harmonic metrics and connections with irregular singularities". Ann. Inst. Fourier (Grenoble) 49 (1999), p. 1265-1291. | DOI | Numdam | EuDML | Zbl | MR

[54] C. Sabbah, "Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere". Russian Math. Surveys 59 (2004). no. 6. p. 1165-1180. arXiv: math.AG/0408294. | DOI | Zbl | MR

[55] C. Sabbah, "Polarizable twistor ūĚíü-modules", pr√©publication, arXiv: math.AG/ 0503038. vi+226 pages. 2005. | Zbl | MR

[56] M. Saito "Modules de Hodge polarisables". Publ. RIMS. Kyoto Univ. 24 (1988), p. 849-995. | DOI | Zbl | MR

[57] M. Saito, "Decomposition theorem for proper K√§hler morphisms", T√īhoku Math. J. 42 (1990), p. 127-147. | DOI | Zbl | MR

[58] M. Saito, "Mixed Hodge Modules". Publ. RIMS. Kyoto Univ. 26 (1990). p. 221-333. | DOI | Zbl | MR

[59] P. Schapira & J.-P. Schneiders Index theorem for elliptic pairs. Astérisque, vol. 224. Société Mathématique de France. Paris. 1994. | Numdam | Zbl

[60] W. Schmid "Variation of Hodge structure: the singularities of the period mapping". Invent. Math. 22 (1973), p. 211-319. | DOI | EuDML | Zbl | MR

[61] C. Simpson "Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization", J. Amer. Math. Soc. 1 (1988), p. 867-918. | DOI | Zbl | MR

[62] C. Simpson, "Harmonic bundles on noncompact curves", J. Amer. Math. Soc. 3 (1990). p. 713-770. | DOI | Zbl | MR

[63] C. Simpson, "Higgs bundles and local systems". Publ. Math. Inst. Hautes √Čtudes Sci. 75 (1992). p. 5-95. | DOI | Numdam | EuDML | Zbl | MR

[64] C. Simpson, "Mixed twistor structures", Prépublication Université de Toulouse & arXiv: math.AG/9705006, 1997.

[65] C. Simpson, "The Hodge filtration on nonabelian cohomology", in Algebraic geometry-Santa Cruz 1995, Proc. of AMS summer conferences. American Mathematical Society, 1997. p. 217-281. | Zbl | MR

[66] J. H. M. Steenbrink "Mixed Hodge structure on the vanishing cohomology", in Real and Complex Singularities, Oslo 1976 (P. Holm, ed.), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, p. 525-563. | DOI | Zbl | MR

[67] J. H. M. Steenbrink & S. Zucker - "Variation of mixed Hodge structurer I", Invent. Math. 80 (1985). p. 489-542. | DOI | EuDML | Zbl | MR

[68] S. Szabo "Nahm transform of meromorphic integrable connections on the Riemann sphere", Thèse, Université Louis Pasteur, Strasbourg, 2005.

[69] M. E. Taylor Pseudodifferential operators, Princeton University Press, Princeton. NJ. 1981. | Zbl | MR

[70] B. Teissier & J.-L. Verdier (eds.) Analyse et topologie sur les espaces singuliers (Luminy, 1981). Astérisque, vol. 101-102. Société Mathématique de France, 1983.

[71] G. N. Watson - A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge. 1922. | MR | JFM

[72] S. Zucker "Hodge theory with degenerating coefficients: L 2 -cohomology in the Poincaré metric", Ann. of Math. 109 (1979), p. 415-476. | DOI | Zbl | MR

[73] K. Zuo Representations of fundamental groups of algebraic varieties, Lect. Notes in Math., vol. 1708, Springer-Verlag, Berlin, Heidelberg, New York, 1999. | MR | Zbl