On a conjecture of Marton

W. T. Gowers; Ben Green; Freddie Manners; Terence Tao

doi:https://doi.org/10.4007/annals.2025.201.2.5

On a conjecture of Marton

Pages 515-549 from Volume 201 (2025), Issue 2 by W. T. Gowers, Ben Green, Freddie Manners, Terence Tao

Abstract

We prove a conjecture of K. Marton, widely known as the polynomial Freiman–Ruzsa conjecture, in characteristic $2$. The argument extends to odd characteristic, with details to follow in a subsequent paper.

Keywords

Freiman's theorem, additive combinatorics, doubling, sumsets

DOI

https://doi.org/10.4007/annals.2025.201.2.5

4880432

zbMATH

8014495

Milestones

Received: 13 December 2023
Revised: 10 October 2024
Accepted: 11 October 2024
Published online: 12 March 2025

Authors

W. T. Gowers

Coll\`{e}ge de France, Paris, France and University of Cambridge, Cambridge, UK

Ben Green

Mathematical Institute, University of Oxford, Oxford, UK

Freddie Manners

University of California San Diego, La Jolla, Ca, USA

Terence Tao

University of California, Los Angeles, CA, USA