• Corpus ID: 211677566

Reduction theory for connections over the formal punctured disc

  title={Reduction theory for connections over the formal punctured disc},
  author={Andres Fernandez Herrero},
  journal={arXiv: Algebraic Geometry},
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state and prove some new quantitative results. 
Tame Parahoric Nonabelian Hodge Correspondence in Positive Characteristic over Algebraic Curves
  • Mao Li, Hao Sun
  • Mathematics
  • 2021
Let G be a reductive group, and let X be an algebraic curve over an algebraically closed field k with positive characteristic. We prove a version of nonabelian Hodge correspondence for Glocal systems


Any flat bundle on a punctured disc has an oper structure
We prove that any flat G-bundle, where G is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the local geometric
Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc
This paper concerns regular connections on trivial algebraic Gprincipal fiber bundles over the infinitesimal punctured disc, where G is a connected reductive linear algebraic group over an
An Introduction to Algebraic Geometry and Algebraic Groups
1. Algebraic sets and algebraic groups 2. Affine varieties and finite morphisms 3. Algebraic representations and Borel subgroups 4. Frobenius maps and finite groups of Lie type Bibliography Index
Local Analytic Geometry
Elementary Theory in Cn Weierstrass Preparation Theorem Review from Local Algebra Parameters in Power Series Rings Analytic Sets Language of Sheaves Analytic Spaces.
Conjugacy classes in semisimple algebraic groups
Review of semisimple groups Basic facts about classes and centralizers Centralizers of semisimple elements The adjoint quotient Regular elements Parabolic subgroups and unipotent classes The
Nilpotent orbits in semisimple Lie algebras
Preliminaries semisimple orbits the Dynkin-konstant Classification principal, subregular, and minimal nilpotent orbits nilpotent orbits in the classical algebras topology of nilpotent orbits induced
Preservation of depth in local geometric Langlands correspondence
It is expected that, under mild conditions, local Langlands correspondence preserves depths of representations. In this article, we formulate a conjectural geometrisation of this expectation. We
Complex analytic connections in fibre bundles
Introduction. In the theory of differentiable fibre bundles, with a Lie group as structure group, the notion of a connection plays an important role. In this paper we shall consider complex analytic