Dr. Brad Drew:
De Rham realizations of mixed motives over general base schemes
Time and place
Friday, 19.4.13, 10:00-11:00, Raum 404, Eckerstr. 1
Abstract
After briefly reviewing the construction of the stable homotopy category SH(X) of a scheme X and the associated formalism of Grothendieck's six functors, I explain how to construct de Rham realization functors from SH(X) into an ind-completion of the bounded derived category of holonomic DX-modules when X is a smooth, quasi-projective C-scheme. As a corollary, the classical Betti-de Rham comparison theorem furnishes a purely algebraic proof of the Riemann-Hilbert correspondence between the full subcategories of D^bc(X(C),C) and D^bhol(DX)$ spanned by the complexes ``of geometric origin''.\n\n