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Some uniform constructibility and calculability results in étale cohomology
【2013.5.10/15/17/22/24 10:00am,C610】

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 2013-4-22 

  Colloquia & Seminars 

  Speaker

      

   Prof.Fabrice Orgogozo, CNRS, école polytechnique

  Title

  

   Some uniform constructibility and calculability results in étale cohomology                       

 

  Time

  2013.5.10/15/17/22/24 10:00am                                   

  Venue

  C610

  Abstract

   

After a brief reminder of classical finiteness results for étale cohomology, we plan to explain some extensions in two directions: uniformity and calculability.

Uniformity. We will prove that the direct image of a "uniformly tame-constructible" family of complexes by a proper morphism is uniformly tame-constructible. This is a generalization of the following fact: if X is a scheme separated of finite type over an algebraically closed field, the mod ? Betti numbers of X are bounded independently of ?. (If time permits, the non-proper case and other 6-operations will be considered.)

Calculability. We will prove the algorithmic computability of the mod ? cohomology of a scheme X (as above), as well as the maps induced by functoriality (e.g. Galois action). An extension to higher direct images of constructible sheaves, with respect to proper morphisms, will also be proven.

  Affiliation

 

 

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