Moduli of vector bundles on curve and semiorthogonal decomposition

Abstract

The present dissertation studies the derived categories of coherent sheaves on various versions of moduli of bundles on an algebraic curve over a field of characteristic $0$, including the full moduli stack, the semistable locus and the coarse moduli space on proper curves and affine curves. We construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. As essential ingredients in the proof, we develop Borel-Weil-Bott theory for loop groups on twisted moduli spaces and derived Schur-Weyl duality for current groups. We also carry out a detailed study the Harder-Narasimhan stratification in the general framework of $\Theta$-stratification.