#### Vol. 15, No. 3, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Computing integral points on $X_{\mathrm{ns}}^+(p)$
569–608

### Aurélien Bajolet, Yuri Bilu and Benjamin Matschke

The Erdős–Selfridge problem with square-free moduli
609–626

### Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe and Marius Tiba

Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families
627–655

### Manjul Bhargava, Zev Klagsbrun, Robert J. Lemke Oliver and Ari Shnidman

Height of rational points on random Fano hypersurfaces
657–672

### Pierre Le Boudec

The geometric average size of Selmer groups over function fields
673–709

### Aaron Landesman

Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant
711–727

### Eric Rains, Karl Rubin, Travis Scholl, Shahed Sharif and Alice Silverberg

The Hodge ring of varieties in positive characteristic
729–745

### Remy van Dobben de Bruyn

Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan
747–771

### Samuel Le Fourn and Pedro Lemos

A note on Lie algebra cohomology
773–783

### Michael J. Larsen and Valery A. Lunts

Skeletons of Prym varieties and Brill–Noether theory
785–820