The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of...
In this paper we begin the study of the (dual) Steenrod algebra of the motivic Witt cohomology spectrum H_Wℤ by determining the algebra structure of H_Wℤ∗∗H_Wℤ over fields k of characteristic not 2 which are extensions of fields F with K^M_2(F)/2=0. For example, this includes all fields of odd characteristic,...
We define multi-indexed Deligne extensions and multi-indexed log-variations of Hodge structures in the category of (filtered) logarithmic D-modules, via the idea of Bernstein– Sato polynomials and Kashiwara–Malgrange filtrations, generalizing the Deligne canonical extensions of flat vector bundles. We also obtain many comparison results with perverse sheaves via the logarithmic de...