Mathematical Research Letters

Volume 29 (2022)

Number 4

Balanced presentations for fundamental groups of curves over finite fields

Pages: 1251 – 1259



Mark Shusterman (Department of Mathematics, University of Wisconsin, Madison, Wisc., U.S.A.)


We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators.

Received 5 December 2020

Accepted 22 January 2021

Published 23 February 2023