Per citar aquest document: http://ddd.uab.cat/record/60925
Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions
Burgos Gil, José Ignacio
Litcanu, R.
Centre de Recerca Matemàtica

Publicació: Centre de Recerca Matemàtica 2010
Descripció: 96 p.
Col·lecció: Prepublicacions del Centre de Recerca Matemàtica ; 926
Resum: We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.
Drets: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Llengua: Anglès.
Document: preprint
Matèria: Arakelov, Teoria d' ; Riemann-Roch, Teoremes de

Adreça alternativa: http://hdl.handle.net/2072/64629


96 p, 757.8 KB

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