Forschung

Publikationen

Fang, Yanbo; Gubler, Walter; Künnemann, Klaus: On the non-archimedean Monge-Ampère equation in mixed characteristic. Preprint 2022. (arXiv)

Burgos Gil, José Igancio; Gubler, Walter; Jell, Philipp; Künnemann, Klaus: Pluripotential theory for tropical toric varieties and non-archimedean Monge-Ampére equations. Preprint 2021 (arXiv)

Burgos Gil, José Igancio; Gubler, Walter; Jell, Philipp; Künnemann, Klaus: A comparison of positivity in complex and tropical toric geometry. Mathematische Zeitschrift, 299 (3), 1199-1255. (arXiv) (doi)

Walter Gubler, Philipp Jell, Klaus Künnemann and Florent Martin: Continuity of Plurisubharmonic Envelopes in Non-Archimedean Geometry and Test Ideals (with an Appendix by José Ignacio Burgos Gil and Martín Sombra). Ann. Inst. Fourier, Grenoble 69, 5 (2019) 2331-2376. (arXiv)??(doi)

Burgos Gil, José Ignacio; Gubler, Walter; Jell, Philipp; Künnemann, Klaus; Martin, Florent: Differentiability of non-archimedean volumes and non-archimedean Monge-Ampère equations (with an appendix by Robert Lazarsfeld). Algebraic Geometry 7 (2) (2020) 113–152.?? (arXiv)? (doi)

Gubler, Walter; Künnemann, Klaus: Positivity properties of metrics and delta-forms. J. reine angew. Math. 752 (2019), 141-177.?? (arXiv)?? (doi)

Gubler, Walter; Künnemann, Klaus: A tropical approach to non-archimedean Arakelov theory. Algebra & Number Theory Vol. 11 (2017), No. 1, 77–180.?? (arXiv)?? (doi)

Bost, Jean-Beno?t; Künnemann, Klaus: Hermitian vector bundles and extension groups on arithmetic schemes. II. The arithmetic Atiyah extension. In: From Probability to Geometry (I). Volume in honor of the 60th birthday of Jean-Michel Bismut (Xianzhe Dai, Rémi Léandre, Xiaonan Ma, Weiping Zhang, editors). Asterisque 327 (2009), 361-424.? ? (arXiv)

Bost, Jean-Beno?t; Künnemann, Klaus: Hermitian vector bundles and extension groups on arithmetic schemes. I. Geometry of numbers. Advances in Mathematics 223 (2010), 987-1106. ? (arXiv) ?? (doi)

Künnemann, Klaus; Tamvakis, Harry: The Hodge star operator on Schubert forms. Topology 41 no. 5 (2002), 945-960.? ? (arXiv) ?? (doi)

Künnemann, Klaus: Height pairings for algebraic cycles on abelian varieties. Ann. Sci. ?cole Norm. Sup. (4) 34 (2001), no. 4, 503-523.? ? (numdam)?? (doi)

Künnemann, Klaus: Uniformization of Shimura curves by the $p$-adic upper half plane. Courbes semi-stables et groupe fondamental en géométrie algébrique (Luminy, 1998), 121--128, Progr. Math., 187, Birkh?user, Basel, 2000.

Künnemann, Klaus: Algebraic cycles on toric fibrations over abelian varieties. Math. Z. 232 (1999), no. 3, 427--435. ?? (doi)

Künnemann, Klaus: Projective regular models for abelian varieties, semistable
reduction, and the height pairing. Duke Math. J. 95 (1998), no. 1, 161--212. ?? (doi)

Künnemann, Klaus: The K?hler identity for bigraded Hodge-Lefschetz modules and its application in non-Archimedean Arakelov geometry. J. Algebraic Geom. 7 (1998), no. 4, 651--672.

Künnemann, Klaus: Higher Picard varieties and the height pairing. Amer. J. Math. 118 (1996), no. 4, 781--797 ?? (doi)

Künnemann, Klaus; Maillot, Vincent:Théorèmes de Lefschetz et de Hodge arithmétiques pour les variétés admettant une décomposition cellulaire. Regulators in analysis, geometry and number theory, 197--205, Progr. Math., 171, Birkh?user Boston, Boston, MA, 2000.? (doi)

Künnemann, Klaus: Some remarks on the arithmetic Hodge index conjecture. Compositio Math. 99 (1995), no. 2, 109--128. ?? (numdam)

Künnemann, Klaus: Arakelov Chow groups of abelian schemes, arithmetic Fourier
transform, and analogues of the standard conjectures of Lefschetz type. Math. Ann. 300 (1994), no. 3, 365--392. ?? (purl)

Künnemann, Klaus: On the Chow motive of an abelian scheme. Motives (Seattle, WA, 1991), 189--205, Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994.? (doi)

Künnemann, Klaus: A Lefschetz decomposition for Chow motives of abelian schemes. Invent. Math. 113 (1993), no. 1, 85--102. ?? (purl)

Künnemann, Klaus: Chow-Motive von abelschen Schemata und die Fouriertransformation. Schriftenreihe des Mathematischen Instituts und des Graduiertenkollegs der Universit?t Münster, 3. Serie, 6. Universit?t Münster, Mathematisches Institut, Münster, 1992. vi+53 pp.

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