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# Vers la forme générale du théorème de Grothendieck-Riemann-Roch

Abstract : The aim of this work is the study of the Grothendieck-Riemann-\-Roch-theorem. Gro\-then\-dieck and his school has proven a quite general form of this theorem in the sixties and also conjectured a much more general form of it. We state a conjecture intermediate between the known results and Grothendieck's most general conjectures. We then prove it in two special cases. More precisely, the conjecture is that Grothendieck-Riemann-Roch theorem is true for a proper and locally complete intersection morphism between two divisorial schemes of equal characteristic. We prove some special cases of this conjecture, in the case of positive characteristic on the one hand, in the case of regular schemes for which the polynomial $T^k-1$ has $k$ roots on the other hand. Grothendieck-Riemann-Roch theorem being equivalent mod. torsion to Adams-Riemann-Roch theorem, we prove Adams-Riemann-Roch type results and deduce from them Grothendieck-Riemann-Roch type results.
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https://tel.archives-ouvertes.fr/tel-00741782
Contributor : Bertrand Duma <>
Submitted on : Monday, October 15, 2012 - 12:11:20 PM
Last modification on : Friday, April 10, 2020 - 5:10:28 PM
Long-term archiving on: : Saturday, December 17, 2016 - 12:50:18 AM

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• HAL Id : tel-00741782, version 1

### Citation

Bertrand Duma. Vers la forme générale du théorème de Grothendieck-Riemann-Roch. Géométrie algébrique [math.AG]. Université Paris-Diderot - Paris VII, 2012. Français. ⟨tel-00741782⟩

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