Universität Augsburg

Professor Dr. DenisCharles Cisinski
Universität Regensburg
spricht am
Dienstag, 21. November 2017
um
15:45 Uhr
im
Raum 3008 (L1)
über das Thema:
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 tstructure 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 tstructure. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Marc NieperWißkirchen 
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).