A geometric analogue of a conjecture of gross and reeder

Masoud Kamgarpour; Daniel S. Sage

doi:10.1353/ajm.2019.0038

A geometric analogue of a conjecture of gross and reeder

Masoud Kamgarpour
, Daniel S. Sage

Mathematics

University of Queensland

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let G be a simple complex algebraic group. We prove that the irregularity of the adjoint connection of an irregular flat G-bundle on the formal punctured disk is always greater than or equal to the rank of G. This can be considered as a geometric analogue of a conjecture of Gross and Reeder. We will also show that the irregular connections with minimum adjoint irregularity are precisely the (formal) Frenkel-Gross connections. As a corollary, we establish the de Rham analogue of a conjecture of Heinloth, Nĝo, and Yun for G = SL_n.

Original language	English
Pages (from-to)	1457-1476
Number of pages	20
Journal	American Journal of Mathematics
Volume	141
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2019.0038
State	Published - Oct 2019

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abstract = "Let G be a simple complex algebraic group. We prove that the irregularity of the adjoint connection of an irregular flat G-bundle on the formal punctured disk is always greater than or equal to the rank of G. This can be considered as a geometric analogue of a conjecture of Gross and Reeder. We will also show that the irregular connections with minimum adjoint irregularity are precisely the (formal) Frenkel-Gross connections. As a corollary, we establish the de Rham analogue of a conjecture of Heinloth, Nĝo, and Yun for G = SLn.",

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AB - Let G be a simple complex algebraic group. We prove that the irregularity of the adjoint connection of an irregular flat G-bundle on the formal punctured disk is always greater than or equal to the rank of G. This can be considered as a geometric analogue of a conjecture of Gross and Reeder. We will also show that the irregular connections with minimum adjoint irregularity are precisely the (formal) Frenkel-Gross connections. As a corollary, we establish the de Rham analogue of a conjecture of Heinloth, Nĝo, and Yun for G = SLn.

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A geometric analogue of a conjecture of gross and reeder

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