English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We use Drinfeld's relative compactifications and the Tannakian viewpoint onprincipal bundles to construct the Harder-Narasimhan stratification of themoduli stack Bun_G of G-bundles on an algebraic curve in arbitrarycharacteristic, generalizing the stratification for G=GL_n due to Harder andNarasimhan to the case of an arbitrary reductive group G. To establish thestratification on the set-theoretic level, we exploit a Tannakianinterpretation of the Bruhat decomposition and give a new and purely geometricproof of the existence and uniqueness of the canonical reduction in arbitrarycharacteristic. We furthermore provide a Tannakian interpretation of thecanonical reduction in characteristic 0 which allows to study its behavior infamilies. The substack structures on the strata are defined directly in termsof Drinfeld's compactifications, which we generalize to the case where thederived group of G is not necessarily simply connected. We furthermore useDrinfeld's compactifications to establish various properties of thestratification, including finer information about the structure of theindividual strata and a simple description of the strata closures. Finally, weintroduce a novel notion of slope for principal bundles which allows for anatural formulation of the reduction theory of arbitrary reductive groups inarbitrary characteristic.

The Harder-Narasimhan stratification of the moduli stack of G-bundles via Drinfeld's compactifications