Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck

• Verfasst von: Bismut, Jean-Michel [VerfasserIn]
• Verfasst von: Shen, Shu [VerfasserIn]
• Verfasst von: Wei, Zhaoting [VerfasserIn]
• Titel: Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
• Verf.angabe: by Jean-Michel Bismut, Shu Shen, Zhaoting Wei
• Verlagsort: Cham
• Verlag: Birkhäuser
• Jahr: 2023
• Umfang: 1 Online-Ressource (X, 184 p. 1 illus.)
• Gesamttitel/Reihe: Progress in Mathematics ; 347
• ISBN: 978-3-031-27234-9
• DOI: doi:10.1007/978-3-031-27234-9
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Bismut, Jean-Michel, 1948 - : Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck. - Cham : Birkhäuser, 2023. - x, 184 Seiten
• K10plus-PPN: 1870735749
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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 many researchers in geometry, analysis, and mathematical physics. .