The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 3, pp. 513-559.

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.

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.

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     author = {Burgos Gil, Jos\'e Ignacio and Freixas i Montplet, Gerard and Li\c{t}canu, R\u{a}zvan},
     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},
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Burgos Gil, José Ignacio; Freixas i Montplet, Gerard; Liţcanu, Răzvan. The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 3, pp. 513-559. doi : 10.5802/afst.1415. http://www.numdam.org/articles/10.5802/afst.1415/

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