In this paper we extend the arithmetic Grothendieck-Riemann-Roch Theorem to projective morphisms between arithmetic varieties that are not necessarily smooth over the complex numbers. The main ingredient of this extension is the theory of generalized holomorphic analytic torsion classes previously developed by the authors.
Dans cet article on étend le théorème de Grothendieck-Riemann-Roch arithmétique aux morphismes projectifs entre variétés arithmétiques qui ne sont pas nécessairement lisses sur les nombres complexes. L’outil principal pour établir cette extension est la théorie des classes généralisées de torsion analytique holomorphe, développée dans les travaux précédents des auteurs.
@article{AFST_2014_6_23_3_513_0,
author = {Jos\'e Ignacio Burgos Gil and Gerard Freixas i Montplet and R\u{a}zvan Li\c{t}canu},
title = {The arithmetic {Grothendieck-Riemann-Roch} theorem for general projective morphisms},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {513--559},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {3},
year = {2014},
doi = {10.5802/afst.1415},
mrnumber = {3266704},
zbl = {06374879},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1415/}
}
TY - JOUR AU - José Ignacio Burgos Gil AU - Gerard Freixas i Montplet AU - Răzvan Liţcanu TI - The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 513 EP - 559 VL - 23 IS - 3 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1415/ DO - 10.5802/afst.1415 LA - en ID - AFST_2014_6_23_3_513_0 ER -
%0 Journal Article %A José Ignacio Burgos Gil %A Gerard Freixas i Montplet %A Răzvan Liţcanu %T The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 513-559 %V 23 %N 3 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1415/ %R 10.5802/afst.1415 %G en %F AFST_2014_6_23_3_513_0
José Ignacio Burgos Gil; Gerard Freixas i Montplet; Răzvan Liţcanu. The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 3, pp. 513-559. doi : 10.5802/afst.1415. https://afst.centre-mersenne.org/articles/10.5802/afst.1415/
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