These lectures will be an introduction to the study of algebraic K-theory and invariants given by algebraic cycles on algebraic varieties. We will be primarily interested in complex, quasi-projective varieties and shall often assume that the varieties are smooth. Algebraic K-groups arise from the study of algebraic vector bundles on algebraic varieties. Algebraic cycles are formal sums of algebraic subvarieties. Both algebraic vector bundles and algebraic cycles are intrinsic, algebraic aspects of an algebraic variety. As seen first in Grothendieck's Riemann Roch theorem, these are closely intertwined. In recent years, higher algebraic K-theory and higher Chow groups (or motivic cohomology) have seen great advances introduced by Bloch, Suslin-Voevodsky, and others. Moreover, there are tantalizing conjectures by Beilinson which present a framework fitting our limited knowledge. My goal is to present some of these exciting ideas, giving an overview and motivation for current work. Time permitting, we shall also survey the A¹ homotopy theory of Morel-Voevodsky and the various semi-topological theories of Friedlander-Walker.
Zeit: Donnerstag 10 - 12
Ort: HG G 43 (Hermann-Weyl-Zimmer)