This project deals with motivic homotopy theory; this is a field seeking to apply methods from algebraic topology to algebraic geometry. We aim to solve several problems in both unstable and stable motivic homotopy theory.Naturally much of our focus is on homotopy sheaves of algebraic varieties; we will study their relationship with A^1-homology sheaves, cellular A^1-homology, stable homotopy sheaves, and also their bearing on the algebraic geometry of the variety. We will also pursue new computations of cellular A^1-homology and prove a cancellation theorem for higher correspondence categories.
DFG Programme
Research Grants
International Connection
India
