Topics in Motivic Homotopy Theory

Abstract

In first half of the work we prove the \A^1 connectivity of moduli stack of vector bundles on a curve, as a consequence of which we classify projective bundles on curves upto their \A^1 homotopy type. Based on joint work with Amit Hogadi. The second part deals with constructing a Gersten complex of a cohomology theory over a general base. We prove the partial exactness of this complex and give conditions for its exactness. Moreover we prove such an exactness holds in case of ́etale cohomology with finite coefficients over a general base, known as Bloch Ogus theorem. Joint work with Neeraj Deshmukh and Girish Kulkarni