Integral representation of moderate cohomology
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 1, pp. 117-137.

Nous faisons la représentation canonique classique de Dickenstein–Sessa dans la cohomologie modérée locale explicite par une formule intégrale. Nous fournissons également une représentation similaire des groupes de cohomologie modérés locaux supérieurs.

We make the classical Dickenstein–Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups.

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DOI : 10.5802/afst.1668
Classification : 32A26, 32A27, 32C25, 32C35
Mots clés : moderate cohomology, integral representation, residue current, coherent ideal sheaf, complex space
Kalm, Håkan Samuelsson 1

1 Håkan Samuelsson Kalm, Department of Mathematical Sciences, Division of Algebra and Geometry, University of Gothenburg and Chalmers University of Technology, SE-412 96 Göteborg, Sweden
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Kalm, Håkan Samuelsson. Integral representation of moderate cohomology. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 1, pp. 117-137. doi : 10.5802/afst.1668. http://archive.numdam.org/articles/10.5802/afst.1668/

[1] Andersson, Mats Integral representation with weights. I, Math. Ann., Volume 326 (2003) no. 1, pp. 1-18 | DOI | MR | Zbl

[2] Andersson, Mats Residue currents and ideals of holomorphic functions, Bull. Sci. Math., Volume 128 (2004) no. 6, pp. 481-512 | DOI | MR | Zbl

[3] Andersson, Mats Residues of holomorphic sections and Lelong currents, Ark. Mat., Volume 43 (2005) no. 2, pp. 201-219 | DOI | MR | Zbl

[4] Andersson, Mats Integral representation with weights. II. Division and interpolation, Math. Z., Volume 254 (2006) no. 2, pp. 315-332 | DOI | MR | Zbl

[5] Andersson, Mats Uniqueness and factorization of Coleff–Herrera currents, Ann. Fac. Sci. Toulouse, Math., Volume 18 (2009) no. 4, pp. 651-661 | DOI | Numdam | MR | Zbl

[6] Andersson, Mats Coleff-Herrera currents, duality, and Noetherian operators, Bull. Soc. Math. Fr., Volume 139 (2011) no. 4, pp. 535-554 | DOI | Numdam | MR | Zbl

[7] Andersson, Mats; Lärkäng, Richard The ¯-equation on a non-reduced analytic space, Math. Ann., Volume 374 (2019) no. 1-2, pp. 553-599 | DOI | MR | Zbl

[8] Andersson, Mats; Samuelsson Kalm, Håkan A Dolbeault–Grothendieck lemma on complex spaces via Koppelman formulas, Invent. Math., Volume 190 (2012) no. 2, pp. 261-297 | DOI | MR | Zbl

[9] Andersson, Mats; Wulcan, Elizabeth Residue currents with prescribed annihilator ideals, Ann. Sci. Éc. Norm. Supér., Volume 40 (2007) no. 6, pp. 985-1007 | DOI | Numdam | MR | Zbl

[10] Andersson, Mats; Wulcan, Elizabeth Decomposition of residue currents, J. Reine Angew. Math., Volume 638 (2010), pp. 103-118 | MR | Zbl

[11] Andersson, Mats; Wulcan, Elizabeth Direct images of semi-meromorphic currents, Ann. Inst. Fourier, Volume 68 (2018) no. 2, pp. 875-900 | DOI | Numdam | MR | Zbl

[12] Barlet, Daniel Le faisceau ω X · sur un espace analytique X de dimension pure, Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977) (Lecture Notes in Mathematics), Volume 670, Springer, 1978, pp. 187-204 | DOI | MR | Zbl

[13] Björk, Jan-Erik Analytic 𝒟-modules and applications, Mathematics and its Applications, 247, Kluwer Academic Publishers Group, Dordrecht, 1993, xiv+581 pages | MR | Zbl

[14] Björk, Jan-Erik Residues and 𝒟-modules, The legacy of Niels Henrik Abel, Springer, 2004, pp. 605-651 | DOI | Zbl

[15] Coleff, Nicolas R.; Herrera, Miguel E. Les courants résiduels associés à une forme méromorphe, Lecture Notes in Mathematics, 633, Springer, 1978, x+211 pages | Zbl

[16] Demailly, Jean-Pierre; Passare, Mikael Courants résiduels et classe fondamentale, Bull. Sci. Math., Volume 119 (1995) no. 1, pp. 85-94 | Zbl

[17] Dickenstein, Carmen Alicia; Sessa Canonical representatives in moderate cohomology, Invent. Math., Volume 80 (1985) no. 3, pp. 417-434 | DOI | MR | Zbl

[18] Dickenstein, Carmen Alicia; Sessa Résidus de formes méromorphes et cohomologie modérée, Géométrie complexe (Paris, 1992) (Actualités Sci. Indust.), Volume 1438, Hermann, 1996, pp. 35-59 | Zbl

[19] Herrera, Miguel E.; Lieberman, David Residues and principal values on complex spaces, Math. Ann., Volume 194 (1971), pp. 259-294 | DOI | MR | Zbl

[20] Hörmander, Lars The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften, 256, Springer, 1990, xii+440 pages (Distribution theory and Fourier analysis) | MR | Zbl

[21] Lärkäng, Richard; Samuelsson Kalm, Håkan Various approaches to products of residue currents, J. Funct. Anal., Volume 264 (2013) no. 1, pp. 118-138 | DOI | MR | Zbl

[22] Lärkäng, Richard; Wulcan, Elizabeth Residue currents and fundamental cycles, Indiana Univ. Math. J., Volume 67 (2018) no. 3, pp. 1085-1114 | DOI | MR | Zbl

[23] Ruppenthal, Jean; Samuelsson Kalm, Håkan; Wulcan, Elizabeth Explicit Serre duality on complex spaces, Adv. Math., Volume 305 (2017), pp. 1320-1355 | DOI | MR | Zbl

[24] Samuelsson Kalm, Håkan The ¯-equation, duality, and holomorphic forms on a reduced complex space, J. Geom. Anal., Volume 31 (2021) no. 2, pp. 1786-1820 | DOI | MR | Zbl

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