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A generalized Hirzebruch Riemann–Roch theorem

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Title: A generalized Hirzebruch Riemann–Roch theorem
Alternate Title: Un théorème de Hirzebruch–Riemann–Roch généralisé
Authors: Ramadoss, Ajay C.1 ajaycr@math.cornell.edu
Source: Comptes Rendus. Mathématique. Mar2009, Vol. 347 Issue 5/6, p289-292. 4p.
Subjects: Riemann-Roch theorems, Homology theory, Hodge theory, Mathematical mappings, Algebraic functions, Algebra
Abstract (English): Abstract: This short Note proves a generalization of the Hirzebruch Riemann–Roch theorem equivalent to the Cardy condition. This is done using an earlier result that explicitly describes what the Mukai pairing on Hochschild homology descends to in Hodge cohomology via the Hochschild–Kostant–Rosenberg map twisted by the root Todd genus. To cite this article: A.C. Ramadoss, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]
Abstract (French): Résumé: Nous montrons dans cette Note une généralisation du théorème de Hirzebruch–Riemann–Roch, équivalente à la condition de Cardy. On s''''appuie pour cela sur un résultat antérieur décrivant l''''accouplement de Mukai sur la cohomologie de Hochschild en termes de la cohomologie de Hodge, via l''''application de Hochschild–Kostant–Rosenberg tordue par le genre de Todd de la base. Pour citer cet article : A.C. Ramadoss, C. R. Acad. Sci. Paris, Ser. I 347 (2009).
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: A generalized Hirzebruch Riemann–Roch theorem
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  Data: Un théorème de Hirzebruch–Riemann–Roch généralisé
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  Data: <searchLink fieldCode="AR" term="%22Ramadoss%2C+Ajay+C%2E%22">Ramadoss, Ajay C.</searchLink><relatesTo>1</relatesTo><i> ajaycr@math.cornell.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Comptes+Rendus%2E+Mathématique%22">Comptes Rendus. Mathématique</searchLink>. Mar2009, Vol. 347 Issue 5/6, p289-292. 4p.
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  Data: <searchLink fieldCode="DE" term="%22Riemann-Roch+theorems%22">Riemann-Roch theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Homology+theory%22">Homology theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hodge+theory%22">Hodge theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+mappings%22">Mathematical mappings</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+functions%22">Algebraic functions</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink>
– Name: Abstract
  Label: Abstract (English)
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  Data: Abstract: This short Note proves a generalization of the Hirzebruch Riemann–Roch theorem equivalent to the Cardy condition. This is done using an earlier result that explicitly describes what the Mukai pairing on Hochschild homology descends to in Hodge cohomology via the Hochschild–Kostant–Rosenberg map twisted by the root Todd genus. To cite this article: A.C. Ramadoss, C. R. Acad. Sci. Paris, Ser. I 347 (2009). [Copyright &y& Elsevier]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Résumé: Nous montrons dans cette Note une généralisation du théorème de Hirzebruch–Riemann–Roch, équivalente à la condition de Cardy. On s''''appuie pour cela sur un résultat antérieur décrivant l''''accouplement de Mukai sur la cohomologie de Hochschild en termes de la cohomologie de Hodge, via l''''application de Hochschild–Kostant–Rosenberg tordue par le genre de Todd de la base. Pour citer cet article : A.C. Ramadoss, C. R. Acad. Sci. Paris, Ser. I 347 (2009). </ce:abst [Copyright 2009 Elsevier]
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
      – SubjectFull: Homology theory
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      – SubjectFull: Hodge theory
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