Théorie de Hodge et correspondance de Hitchin-Kobayashi sauvages [d'après T. Mochizuchi]
Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Talk no. 1050, 37 p.
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Sabbah, Claude. Théorie de Hodge et correspondance de Hitchin-Kobayashi sauvages [d'après T. Mochizuchi], in Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Talk no. 1050, 37 p. http://archive.numdam.org/item/AST_2013__352__205_0/

[1] D. G. Babbitt & V. S. Varadarajan - Local moduli for meromorphic differential equations, Astérisque 169-170 (1989). | Numdam | Zbl

[2] A. A. Beilinson, J. N. Bernstein & P. Deligne - Faisceaux pervers, Astérisque 100 (1982), p. 7-171. | Numdam | MR | Zbl

[3] O. Biquard - Fibrés paraboliques stables et connexions singulières plates, Bull. Soc. math. France 119 (1991), p. 231-257. | DOI | EuDML | Numdam | MR | Zbl

[4] O. Biquard, Fibrés de Higgs et connexions intégrables : le cas logarithmique (diviseur lisse), Ann. Sci. École Norm. Sup. 30 (1997), p. 41-96. | DOI | EuDML | Numdam | MR | Zbl

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

[6] G. Böckle & C. Khare - Mod representations of arithmetic fundamental groups. II. A conjecture of A.J. de Jong, Compositio Math. 142 (2006), n° 2, p. 271-294. | DOI | MR | Zbl

[7] N. Borne - Sur les représentations du groupe fondamental d'une variété privée d'un diviseur à croisements normaux simples, Indiana Univ. Math. J. 58 (2009), n° 1, p. 137-180. | DOI | MR | Zbl

[8] E. Cattani & A. Kaplan - Polarized mixed Hodge structure and the monodromy of a variation of Hodge structure, Invent. Math. 67 (1982), p. 101-115. | DOI | EuDML | MR | Zbl

[9] E. Cattani, A. Kaplan & W. Schmid - Degeneration of Hodge structures, Ann. of Math. 123 (1986), p. 457-535. | DOI | MR | Zbl

[10] 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 | MR | Zbl

[11] S. Cecotti, P. Fendley, K. Intriligator & C. Vafa - A new supersymmetric index, Nuclear Phys. B 386 (1992), p. 405-452. | DOI | MR

[12] S. Cecotti & C. Vafa - Topological-antitopological fusion, Nuclear Phys. B 367 (1991), p. 359-461. | DOI | MR | Zbl

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

[15] M. A. De Cataldo & L. Migliorini - The Hodge theory of algebraic maps, Ann. Sci. École Norm. Sup. 38 (2005), n° 5, p. 693-750. | DOI | EuDML | Numdam | MR | Zbl

[16] M. A. De Cataldo & L. Migliorini, The decomposition theorem, perverse sheaves and the topology of algebraic maps, Bull. Amer. Math. Soc. 46 (2009), n° 4, p. 535-633. | DOI | MR | Zbl

[17] P. Deligne - Equations différentielles à points singuliers réguliers, Lect. Notes in Math., vol. 163, Springer, 1970. | MR | Zbl

[18] P. Deligne, Théorie de Hodge. I, in Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, 1971, p. 425-430. | MR | Zbl

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

[20] P. Deligne, Lettre à B. Malgrange du 19/4/1978, Documents mathématiques 5 (2007), p. 25-26.

[21] P. Deligne, Lettre à B. Malgrange du 20/12/1983, Documents mathématiques 5 (2007), p. 37-41.

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

[23] D. Gaitsgory - On De Jong's conjecture, Israel J. Math. 157 (2007), p. 155-191. | DOI | MR | Zbl

[24] M. Goresky & R. D. Macpherson Intersection homology II, Invent. Math. 71 (1983), p. 77-129. | DOI | EuDML | MR | Zbl

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

[26] C. Hertling & Ch. Sevenheck - Limits of families of Brieskorn lattices and compactified classifying spaces, Adv. in Math. 223 (2010), p. 1155-1224. | DOI | MR | Zbl

[27] N. J. Hitchin - The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), n° 1, p. 59-126. | DOI | MR | Zbl

[28] W. Hodge - The topological invariants of algebraic varieties, in Proceedings of the International Congress of Mathematicians (Cambridge, Mass., 1950), vol. 1, Amer. Math. Soc., 1952, p. 182-192. | MR | Zbl

[29] H. Iritani - An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. in Math. 222 (2009), n° 3, p. 1016-1079. | DOI | MR | Zbl

[30] H. Iritani, tt * -geometry in quantum cohomology, prépublication arXiv:0906.1307.

[31] J. Iyer & C. Simpson - A relation between the parabolic Chern characters of the de Rham bundles, Math. Ann. 338 (2007), n° 2, p. 347-383. | DOI | MR | Zbl

[32] A. J. De Jong - A conjecture on arithmetic fundamental groups, Israel J. Math. 121 (2001), p. 61-84. | DOI | MR | Zbl

[33] J. Jost, Y.-H. Yang & K. Zuo - Cohomologies of unipotent harmonic bundles over noncompact curves, J. reine angew. Math. 609 (2007), p. 137-159. | MR | Zbl

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

[35] M. Kashiwara - The Riemann-Hilbert problem for holonomic systems, Publ. RIMS, Kyoto Univ. 20 (1984), p. 319-365. | DOI | MR | Zbl

[36] M. Kashiwara, The asymptotic behaviour of a variation of polarized Hodge structure, Publ. RIMS, Kyoto Univ. 21 (1985), p. 853-875. | DOI | MR | Zbl

[37] M. Kashiwara, Semisimple holonomic 𝒟-modules, in Topological Field Theory, Primitive Forms and Related Topics (M. Kashiwara, K. Saito, A. Matsuo & I. Satake, éds.), Progress in Math., vol. 160, Birkhäuser, 1998, p. 267-271. | DOI | MR | Zbl

[38] M. Kashiwara & T. Kawai - On the holonomic systems of differential equations (systems with regular singularities) III, Publ. RIMS, Kyoto Univ. 17 (1981), p. 813-979. | DOI | MR | Zbl

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

[40] L. Katzarkov, M. Kontsevich & T. Pantev - Hodge theoretic aspects of mirror symmetry, in From Hodge theory to integrability and TQFT : tt * -geometry (R. Donagi & K. Wendland, éds.), Proc. Symposia in Pure Math., vol. 78, Amer. Math. Soc., 2008, p. 87-174. | DOI | MR | Zbl

[41] K. Kedlaya - Good formal structures for flat meromorphic connections, I : surfaces, Duke Math. J. 154 (2010), n° 2, p. 343-418. | DOI | MR | Zbl

[42] K. Kedlaya, Good formal structures for flat meromorphic connections, II : excellent schemes, J. Amer. Math. Soc. 24 (2011), n° 1, p. 183-229. | DOI | MR | Zbl

[43] T. Krämer & R. Weissauer - Vanishing theorems for constructible sheaves on abelian varieties, prépublication arXiv:1111.4947. | DOI | MR | Zbl

[44] A. H. M. Levelt & A. Van Den Essen - Irregular singularities in several variables, Mem. Amer. Math. Soc., vol. 40, no. 270, Amer. Math. Soc., 1982. | MR | Zbl

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

[46] B. Malgrange - Équations différentielles à coefficients polynomiaux, Progress in Math., vol. 96, Birkhäuser, 1991. | MR | Zbl

[47] B. Malgrange, Connexions méromorphes, II : le réseau canonique, Invent. Math. 124 (1996), p. 367-387. | DOI | MR | Zbl

[48] Z. Mebkhout - Une équivalence de catégories, Compositio Math. 51 (1984), p. 55-62. | EuDML | Numdam | MR | Zbl

[49] Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984) , p. 63-68. | EuDML | Numdam | MR | Zbl

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

[51] T. Mochizuki, Kobayashi-Hitchin correspondence for tame harmonic bundles and anapplication, Astérisque, vol. 309, Société Mathématique de France, 2006. | Numdam | MR | Zbl

[52] T. Mochizuki, Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules, vol. 185, Mem. Amer. Math. Soc., n° 869-870, Amer. Math. Soc., 2007. | MR | Zbl

[53] T. Mochizuki, Good formal structure for meromorphic flat connections on smooth projective surfaces, in Algebraic Analysis and Around, Advanced Studies in Pure Math., vol. 54, Math. Soc. Japan, 2009, p. 223-253. | MR | Zbl

[54] T. Mochizuki, Kobayashi-Hitchin correspondence for tame harmonic bundles. II, Geom. Topol. 13 (2009), n° 1, p. 359-455. | DOI | MR | Zbl

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

[56] T. Mochizuki, Asymptotic behaviour of variation of pure polarized TERP structures, Publ. RIMS, Kyoto Univ. 47 (2011) , n° 2, p. 419-534. | DOI | MR | Zbl

[57] T. Mochizuki, Stokes structure of a good meromorphic flat bundle, Journal de l'Institut mathématique de Jussieu 10 (2011) , n° 3, p. 675-712. | DOI | MR | Zbl

[58] T. Mochizuki, Mixed twistor D-Modules, prépublication arXiv: 1104.3366. | DOI | MR | Zbl

[59] T. Mochizuki, Holonomic 𝒟-modules with Betti structure, prépublication arXiv: 1001.2336. | Numdam | MR

[60] T. Reichelt & Ch. Sevenheck - Logarithmic Frobenius manifolds, hypergeometric systems and quantum 𝒟 -modules, prépublication arXiv: 1010.2118. | DOI | MR | Zbl

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

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

[63] C. Sabbah, Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere, Russian Math. Surveys 59 (2004), n° 6, p. 1165-1180 | DOI | MR | Zbl

[63] C. Sabbah, Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere, II, Moscow Math. J. 9 (2009) n° 4, p. 885-898. | DOI | MR | Zbl

[64] C. Sabbah, Polarizable twistor 𝒟-modules, Astérisque, vol. 300, Société Mathématique de France, 2005. | Numdam | MR | Zbl

[65] C. Sabbah, Fourier-Laplace transform of a variation of polarized complex Hodge structure, J. reine angew. Math. 621 (2008) , p. 123-158. | MR | Zbl

[66] C. Sabbah, Wild twistor 𝒟-modules, in Algebraic Analysis and Around, Advanced Studies in Pure Math., vol. 54, Math. Soc. Japan, 2009, p. 293-353. | MR | Zbl

[67] C. Sabbah, Fourier-Laplace transform of a variation of polarized complex Hodge structure, II, in New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry (Kyoto, January 2008), Advanced Studies in Pure Math., vol. 59, Math. Soc. Japan, 2010, p. 289-347. | MR | Zbl

[68] C. Sabbah, Non-commutative Hodge structures, à paraître dans Ann. Inst. Fourier. | EuDML | Numdam | MR | Zbl

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

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

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

[72] 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 | MR | Zbl

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

[74] C. Simpson, Higgs bundles and local systems, Publ. Math. Inst. Hautes Études Sci. 75 (1992), p. 5-95. | DOI | Numdam | Zbl

[75] W. Schmid, Mixed twistor structures, prépublication Université de Toulouse & arXiv:math.AG/9705006, 1997.

[76] S. Szabo - Nahm transform for integrable connections on the Riemann sphere, Mém. Soc. Math. France, vol. 110, Société Mathématique de France, 2007. | Numdam | MR | Zbl

[77] V. E. Zakharov & A. V. Mikhailov - Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Soviet Phys. JETP 74 (1978), n° 6, p. 1953-1973. | MR

[78] V. E. Zakharov & A. B. Shabat - Integration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem. II, Funktsional. Anal. i Prilozhen. 13 (1979), n° 3, p. 13-22. | DOI | MR | Zbl

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