Volume 199, Issue 1 – January 2024

A reverse Minkowski theorem

Pages 1-49 by Oded Regev, Noah Stephens-Davidowitz

Purity for flat cohomology

Pages 51-180 by Kęstutis Česnavičius, Peter Scholze

Proof of the simplicity conjecture

Pages 181-257 by Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini

Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a matroid

Pages 259-299 by Nima Anari, Kuikui Liu, Shayan Oveis Gharan, Cynthia Vinzant

Nonabelian level structures, Nielsen equivalence, and Markoff triples

Pages 301-443 by William Y. Chen

Motivic invariants of birational maps

Pages 445-478 by Hsueh-Yung Lin, Evgeny Shinder

Corrigendum: Marginal triviality of the scaling limits of critical 4D Ising and $\phi _4^4$ models

Pages 479-479 by Michael Aizenman, Hugo Duminil-Copin

Erratum to “Special subvarieties of non-arithmetic ball quotients\ and Hodge theory”

Pages 481-481 by Gregorio Baldi, Emmanuel Ullmo