---
title: "Local systems and Suzuki groups"
authors:
  - "Levent Alpoge"
  - "Nicholas M. Katz"
  - "Gabriel Navarro"
  - "Eamonn A. O'Brien"
  - "Pham Huu Tiep"
year: 2023
venue: "arXiv preprint"
arxiv: "2305.03168"
doi: null
source: "https://arxiv.org/abs/2305.03168"
topics:
  - "number-theory"
  - "arithmetic-geometry"
seed_rank: 1202
seed_batch: "alpoge-math-2026-08-24"
reviewed: "2026-08-24"
pool: "maths-foundations"
relevance_score: 9
lineage: arithmetic-geometry
cites:
  []
see:
  - "1197-the-3-4-infinity-modular-family-of-2-tori-completed-at-its-thr"
---

# Local systems and Suzuki groups

## One-sentence takeaway

Geometric monodromy of Katz's rank-sqrt(q)(q-1) local systems F_q on A^1 over F_2 is either the Suzuki group ^2B_2(q) or SL_D; for q=8 it is Suzuki, with arithmetic monodromy the full automorphism group — Katz's conjecture in that case.

## Why it's lovely

Rare collaboration of Alpoge with Katz / Navarro / O'Brien / Tiep: finite groups of Lie type as monodromy, not Selmer averages.

## Problem

Ka-ERS constructed local systems F_q, q=2^{2n+1}. Identify G_geo.

## Design

Group-theoretic constraints on possible geometric monodromy plus computer/character-table checks for q=8.

## Evidence

arXiv:2305.03168, v2 11 May 2023.

## Limitations

Dichotomy not resolved for general q. Not arithmetic statistics.

## Implications for Broadside

Keep for completeness of the Alpoge corpus. Different flavour from the Selmer/Mordell cards.

## Bottom line

Mint 2305.03168.

## Links

- arXiv: [2305.03168](https://arxiv.org/abs/2305.03168)