Resumen de The Harder–Narasimhan stratification of the moduli stack of GG-bundles via Drinfeld’s compactifications

Simon Schieder

• We use Drinfeld’s relative compactifications Bun¯¯¯¯¯¯¯¯¯PBun¯P and the Tannakian viewpoint on principal bundles to construct the Harder–Narasimhan stratification of the moduli stack BunGBunG of GG -bundles on an algebraic curve in arbitrary characteristic, generalizing the stratification for G=GLnG=GLn due to Harder and Narasimhan to the case of an arbitrary reductive group GG . To establish the stratification on the set-theoretic level, we exploit a Tannakian interpretation of the Bruhat decomposition and give a new and purely geometric proof of the existence and uniqueness of the canonical reduction in arbitrary characteristic. We furthermore provide a Tannakian interpretation of the canonical reduction in characteristic 00 which allows to study its behavior in families. The substack structures on the strata are defined directly in terms of Drinfeld’s compactifications Bun¯¯¯¯¯¯¯¯¯PBun¯P , which we generalize to the case where the derived group of GG is not necessarily simply connected. Using Bun¯¯¯¯¯¯¯¯¯PBun¯P , we establish various properties of the stratification, including finer information about the structure of the individual strata and a simple description of the strata closures.