Rigid local systems with monodromy group the Conway group Co3

Nicholas M. Katz; Antonio Rojas-León; Pham Huu Tiep

doi:10.1016/j.jnt.2019.06.016

Rigid local systems with monodromy group the Conway group Co₃

Nicholas M. Katz
, Antonio Rojas-León
, Pham Huu Tiep

Mathematics

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

8 Scopus citations

Abstract

We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic p>0. We then apply them to exhibit a number of rigid local systems of rank 23 on the affine line in characteristic p=3 whose arithmetic and geometric monodromy groups are the Conway group Co₃ in its orthogonal irreducible representation of degree 23.

Original language	English (US)
Pages (from-to)	1-23
Number of pages	23
Journal	Journal of Number Theory
Volume	206
DOIs	https://doi.org/10.1016/j.jnt.2019.06.016
State	Published - Jan 2020

Keywords

Exponential sums
Monodromy
Representation theory
Sporadic groups

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jnt.2019.06.016

Cite this

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title = "Rigid local systems with monodromy group the Conway group Co3 ",

abstract = "We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic p>0. We then apply them to exhibit a number of rigid local systems of rank 23 on the affine line in characteristic p=3 whose arithmetic and geometric monodromy groups are the Conway group Co3 in its orthogonal irreducible representation of degree 23.",

keywords = "Exponential sums, Monodromy, Representation theory, Sporadic groups",

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AU - Rojas-León, Antonio

AU - Tiep, Pham Huu

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N2 - We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic p>0. We then apply them to exhibit a number of rigid local systems of rank 23 on the affine line in characteristic p=3 whose arithmetic and geometric monodromy groups are the Conway group Co3 in its orthogonal irreducible representation of degree 23.

AB - We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic p>0. We then apply them to exhibit a number of rigid local systems of rank 23 on the affine line in characteristic p=3 whose arithmetic and geometric monodromy groups are the Conway group Co3 in its orthogonal irreducible representation of degree 23.

KW - Exponential sums

KW - Monodromy

KW - Representation theory

KW - Sporadic groups

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