Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck (Progress in Mathematics) - Hardcover

Bismut, Jean-Michel; Shen, Shu; Wei, Zhaoting

Hardcover

ISBN 10: 3031272331 ISBN 13: 9783031272332

Verlag: Springer-Verlag GmbH, 2023

Inhaltsangabe

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.

Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource formany researchers in geometry, analysis, and mathematical physics.

Über diesen Titel

Über die Autorin bzw. den Autor

Jean-Michel Bismut is Professor of Mathematics at Université Paris-Sud (Orsay) and a member of the Académie des Sciences. Starting with a background in probability, he has worked extensively on index theory. With Gillet, Soulé, and Lebeau, he contributed to the proof of a theorem of Riemann-Roch-Grothendieck in Arakelov geometry. More recently, he has developed a theory of the hypoelliptic Laplacian, a family of operators that deforms the classical Laplacian, and provides a link between spectral theory and dynamical systems.

Von der hinteren Coverseite

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.
Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for manyresearchers in geometry, analysis, and mathematical physics.

Details zur Ausgabe

• Verlag: Springer-Verlag GmbH
• Erscheinungsdatum: 2023
• Sprache: Englisch
• ISBN 10: 3031272331
• ISBN 13: 9783031272332
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 196
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland