Schematic Harder-Narasimhan stratification for families of principal bundles and Lambda-modules

作者：Gurjar Sudarshan^*; Nitsure Nitin

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2014, 124(3): 315-332.

DOI：10.1007/s12044-014-0165-8

• Principal G-bundle
• Harder-Narasimhan type
• canonical reduction

Let G be a reductive algebraic group over a field k of characteristic zero, let X -%26gt; S be a smooth projective family of curves over k, and let E be a principal G bundle on X. The main result of this note is that for each Harder-Narasimhan type tau there exists a locally closed subscheme S (tau) (E) of S which satisfies the following universal property. If f : T -%26gt; S is any base-change, then f factors via S (tau) (E) if and only if the pullback family f (au) E admits a relative canonical reduction of Harder-Narasimhan type tau. As a consequence, all principal bundles of a fixed Harder-Narasimhan type form an Artin stack. We also show the existence of a schematic Harder-Narasimhan stratification for flat families of pure sheaves of I %26gt;-modules (in the sense of Simpson) in arbitrary dimensions and in mixed characteristic, generalizing the result for sheaves of oe%26quot;-modules proved earlier by Nitsure. This again has the implication that I %26gt;-modules of a fixed Harder-Narasimhan type form an Artin stack.

• 出版日期2014-8