On a conjecture of Marton

From To appear in forthcoming issues 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.

Milestones
Received: 13 December 2023
Revised: 10 October 2024
Accepted: 11 October 2024

Authors

W. T. Gowers

Collegè de France, 11, Place de Marcelin-Berthelot, 75231 Paris 05, France and Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

Ben Green

Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Rd., Oxford OX2 6QW, United Kingdom

Freddie Manners

Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112

Terence Tao

UCLA, Department of Mathematics, Math Sciences Building, 520 Portola Plaza, Box 951555, Los Angeles, CA 90095-1555, USA