Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar zur Algebra und Zahlentheorie

 

Professor Dr. Denis-Charles Cisinski
Universität Regensburg

 
spricht am
 
Dienstag, 21. November 2017
 
um
 
15:45 Uhr
 
im
 
Raum 3008 (L1)
 
über das Thema:
 

»Motivic approximation of Betti numbers«

Abstract:
After the work of Voevodsky and his followers, there is a suitable triangulated category of motives, out of which one can define many numerical invariants, such as Euler characteristics, Lefschetz numbers, or Zeta functions, independently of their realizations (i.e. without choosing a Weil cohomology, such as de Rham or etale cohomology, for instance). However, there is no abelian category of motives yet (in technical terms, there is no known reasonable t-structure on Voevodsky's category). This means that, if we want to compute Betti numbers (the rank of a cohomology group in each degree), there is no available method, except Deligne's proof of the Weil conjectures, which provides such an information in the case of motives of smooth and proper schemes over a finite field. The next best thing consists to approximate Betti numbers independently of their realizations, which has been done by Katz and Laumon a while ago, in terms of etale cohomology. In this talk, I shall explain a motivic version of Deligne's generic base change theorem. The latter allows to promote a fundamental theorem of Beillinson, out of which on can extract a filtration of any geometric motive whose graded pieces are cohomologically concentrated in a single degree. This gives a geometric interpretation of the results of Katz and Laumon. This also provides a way to actually construct candidates for the motivic t-structure.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Marc Nieper-Wißkirchen
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



wwwadm@Math.Uni-Augsburg.DE,    Mi 18-Okt-2017 12:24:48 MESZ