• Download PDF
• Download TeX
• Download bibTeX entry

Metadata

Abstract

References

[Ati76] Atiyah, Michael F. Elliptic operators, discrete groups and Von Neumann algebras, Colloque “Analyse et Topologie” en l’honneur de Henri Cartan, Société Mathématique de France, 1976, pp. 43-72 | Zbl | Numdam

[BBD82] Beĭlinson, Alexander A.; Bernstein, Joseph; Deligne, Pierre Faisceaux Pervers, Analysis and topology on singular spaces, I (Luminy, 1981) (Astérisque), Volume 100, Société Mathématique de France, 1982, pp. 3-171 | MR | Zbl

[BDET24] Bei, Francesco; Diverio, Simone; Eyssidieux, Philippe; Trapani, Stefano Weakly Kähler hyperbolic manifolds and the Green–Griffiths–Lang conjecture, J. Reine Angew. Math., Volume 807 (2024), pp. 257-297 | DOI | Zbl | MR

[Bjö93] Björk, Jan-Erik Analytic $D$-modules and applications, Mathematics and its Applications (Dordrecht), 247, Kluwer Academic Publishers, 1993 | Zbl | DOI | MR

[BL92] Brüning, Jochen; Lesch, Matthias Hilbert complexes, J. Funct. Anal., Volume 108 (1992) no. 1, pp. 88-132 | DOI | Zbl | MR

[Bra21] Braun, Lukas The local fundamental group of a Kawamata log terminal singularity is finite, Invent. Math., Volume 226 (2021) no. 3, pp. 845-896 | DOI | Zbl | MR

[Cam94] Campana, Fredéric Remarks on the universal covering of compact Kähler manifolds, Bull. Soc. Math. Fr., Volume 122 (1994) no. 2, pp. 255-284 | DOI | Zbl | MR

[Cam95] Campana, Fredéric Fundamental group and positivity of cotangent bundles of compact Kähler manifolds, J. Algebr. Geom., Volume 4 (1995) no. 3, pp. 487-502 | Zbl | MR

[Cam01] Campana, Fredéric Cohomologie $L^2$ sur les revêtements d’une variété complexe compacte, Ark. Mat., Volume 39 (2001) no. 2, pp. 263-282 | DOI | Zbl

[CG86] Cheeger, Jeff; Gromov, Mikhael L. $L_2$-cohomology and group cohomology, Topology, Volume 25 (1986), pp. 189-215 | DOI | Zbl | MR

[CKS87] Cattani, Eduardo; Kaplan, Aroldo; Schmid, Wilfried $L_2$ and intersection cohomology for a polarizable Variation of Hodge Structure, Invent. Math., Volume 87 (1987), pp. 217-252 | DOI | Zbl | MR

[Cur14] Curry, Justin Sheaves, Cosheaves and Verdier Duality (2014) (https://arxiv.org/abs/1303.3255v2)

[Cur18] Curry, Justin Dualities between cellular sheaves and cosheaves, J. Pure Appl. Algebra, Volume 222 (2018) no. 4, pp. 966-993 | DOI | Zbl | MR

[Del71] Deligne, Pierre Théorie de Hodge II, Publ. Math., Inst. Hautes Étud. Sci., Volume 40 (1971), pp. 5-57 | DOI | Zbl | MR | Numdam

[Del74] Deligne, Pierre Théorie de Hodge III, Publ. Math., Inst. Hautes Étud. Sci., Volume 44 (1974), pp. 5-77 | DOI | Zbl | MR | Numdam

[Dem] Demailly, Jean-Pierre Complex Analytic and Differential Geometry (https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/)

[Din13] Dingoyan, Pascal Some mixed Hodge structures on $l^2$-cohomology groups of coverings of Kähler manifolds, Math. Ann., Volume 357 (2013) no. 3, pp. 1119-1174 | DOI | Zbl | MR

[Dod77] Dodziuk, Jozef De Rham–Hodge theory for $L^2$-cohomology of infinite coverings, Topology, Volume 16 (1977), pp. 157-165 | DOI | Zbl | MR

[Eys97] Eyssidieux, Philippe La caractéristique d’Euler du complexe de Gauss–Manin, J. Reine Angew. Math., Volume 490 (1997), pp. 155-212 | DOI | Zbl | MR

[Eys98] Eyssidieux, Philippe Un théorème de Nakai–Moishezon pour certaines classes de type $(1,1)$ (1998) (prépublication no. 133 du Laboratoire Emile Picard, https://arxiv.org/abs/math/9811065)

[Eys99] Eyssidieux, Philippe Systèmes linéaires adjoints $L_2$, Ann. Inst. Fourier, Volume 49 (1999) no. 1, pp. 141-176 | DOI | Zbl | MR | Numdam

[Eys00] Eyssidieux, Philippe Invariants de Von Neumann des faisceaux analytiques cohérents, Math. Ann., Volume 317 (2000) no. 3, pp. 527-566 | DOI | Zbl | MR

[Far96] Farber, Michael S. Homological algebra of Novikov–Shubin invariants and Morse inequalities, Geom. Funct. Anal., Volume 6 (1996) no. 4, pp. 628-665 | DOI | Zbl | MR

[God73] Godement, Roger Topologie algébrique et théorie des faisceaux, Publications de l’Institut de mathématique de l’Université de Strasbourg, 13, Hermann, 1973 | Zbl | MR

[GR65] Gunning, Robert C.; Rossi, Hugo Analytic functions of several complex variables, Prentice Hall Series in Modern Analysis, Prentice Hall, 1965 | Zbl | MR

[Gri66] Griffin, Ernest L. jun. Everywhere defined Linear transformations affiliated to the rings of operators, Pac. J. Math., Volume 18 (1966), pp. 489-493 | DOI | Zbl | MR

[Gro91] Gromov, Mikhael L. Kähler hyperbolicity and $L_2$-Hodge theory, J. Differ. Geom., Volume 33 (1991) no. 1, pp. 263-292 | DOI | Zbl | MR

[Har66] Hartshorne, Robin Residues and duality, Lecture Notes in Mathematics, 20, Springer, 1966 | DOI | Zbl | MR

[Hou73] Houzel, Christian Espaces analytiques relatifs et théorèmes de finitude, Math. Ann., Volume 205 (1973), pp. 13-54 | DOI | Zbl | MR

[Jea22] Jean, Bastien $L^2$-cohomology of a variation of Hodge structure for an infinite covering of an open curve ramified at infinity (2022) (https://arxiv.org/abs/2211.11605)

[Kas80] Kashiwara, Masaki Faisceaux constructibles et systèmes holonomes d’équations aux dérivées partielles linéaires à points singuliers réguliers, Séminaire Goulaouic–Schwartz (1979-1980) (Séminaire Équations aux dérivées partielles), École Polytechnique, Centre de Mathématiques, 1980, pp. 1-6 (Exposé 19) | Zbl | MR | Numdam

[KK87] Kashiwara, Masaki; Kawai, Takahiro The Poincaré lemma for variations of polarized Hodge structure, Publ. Res. Inst. Math. Sci., Volume 23 (1987) no. 2, pp. 345-407 | DOI | Zbl | MR

[Kol93] Kollár, János Shafarevich maps and plurigenera of algebraic varieties, Invent. Math., Volume 113 (1993) no. 1, pp. 177-215 | DOI | Zbl | MR

[Kol95] Kollár, János Shafarevich maps and Automorphic Forms, M. B. Porter Lectures, Princeton University Press, 1995 | Zbl | DOI | MR

[KS90] Kashiwara, Masaki; Schapira, Pierre Sheaves on Manifolds, Grundlehren der Mathematischen Wissenschaften, 292, Springer, 1990 | Zbl | DOI | MR

[Lüc02] Lück, Wolfgang $L^2$-invariants: Theory and Applications to Geometry and $K$-theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 44, Springer, 2002 | Zbl | MR

[MNM93] Mebkhout, Zoghman; Narváez-Macarro, Luis The constructibility theorem of Kashiwara, Images directes et constructibilité. Cours d’été du CIMPA “Éléments de la théorie des systèmes différentiels”, août et septembre 1990, Nice, France, Hermann, 1993, pp. 47-98 | Zbl

[Nor02] Nori, Madhav V. Constructible Sheaves, Proceedings of the international colloquium on algebra, arithmetic and geometry, Mumbai, India, January 4–12, 2000. Parts I and II, Narosa Publishing House; Tata Institute of Fundamental Research (2002), pp. 471-491 | Zbl | MR

[Sai89] Saito, Morihiko Induced $𝒟$-modules and differential complexes, Bull. Soc. Math. Fr., Volume 117 (1989) no. 3, pp. 361-387 | DOI | Zbl | MR

[Sai90] Saito, Morihiko Mixed Hodge Modules, Publ. Res. Inst. Math. Sci., Volume 26 (1990), pp. 221-333 | DOI | Zbl | MR

[Sch94] Schneiders, Jean-Pierre A Coherence criterion for Fréchet Modules, Index Theorem for elliptic pairs (Astérisque), Volume 224, Société Mathématique de France, 1994, pp. 99-113 | Zbl | Numdam

[Sch98] Schneider, Peter Verdier Duality on the building, J. Reine Angew. Math., Volume 494 (1998), pp. 205-218 | DOI | Zbl | MR

[Sch99] Schneiders, Jean-Pierre Quasi abelian categories and sheaves, Mémoires de la Société Mathématique de France. Nouvelle Série, 76, Société Mathématique de France, 1999 | Zbl | Numdam

[She85] Shepard, Allen D. A cellular description of the derived category of a stratified space, Ph. D. Thesis, Brown University, Providence, Rhode Island, USA (1985)

[Shu95] Shubin, Mikhail A. $L^2$ Riemann–Roch operators for elliptic operators, Geom. Funct. Anal., Volume 5 (1995) no. 2, pp. 482-527 | DOI | Zbl

[SS] Sabbah, Claude; Schnell, Christian The MHM project Version 2 (Notes available on C. Sabbah’s homepage https://www.cmls.polytechnique.fr/cmat/sabbah/programmes.html, version of 2022/01/13)

[SZ21] Shentu, Junchao; Zhao, Chen $L^2$ representations of Hodge Modules (2021) (https://arxiv.org/abs/2103.04030) | Zbl

[Tak99] Takayama, Shigeharu Nonvanishing theorems on an algebraic variety with large fundamental group, J. Algebr. Geom., Volume 8 (1999) no. 1, pp. 181-195 | Zbl | MR

[Zuc79] Zucker, Steven Hodge theory with degenerating coefficients: $L_2$ cohomology in the Poincaré metric, Ann. Math. (2), Volume 109 (1979), pp. 415-476 | DOI | Zbl | MR