#### Vol. 7, No. 5, 2013

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors' Addresses Editors' Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Ethics Statement Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Other MSP Journals
Sharp upper bounds for the Betti numbers of a given Hilbert polynomial
1019–1064

### Giulio Caviglia and Satoshi Murai

Comparing numerical dimensions
1065–1100

### Brian Lehmann

Some consequences of a formula of Mazur and Rubin for arithmetic local constants
1101–1120

### Jan Nekovář

Quantized mixed tensor space and Schur–Weyl duality
1121–1146

### Richard Dipper, Stephen Doty and Friederike Stoll

Weakly commensurable $S$-arithmetic subgroups in almost simple algebraic groups of types $\mathsf{B}$ and $\mathsf{C}$
1147–1178

### Skip Garibaldi and Andrei Rapinchuk

Minimisation and reduction of 5-coverings of elliptic curves
1179–1205

### Tom Fisher

On binary cyclotomic polynomials
1207–1223

### Étienne Fouvry

Local and global canonical height functions for affine space regular automorphisms
1225–1252

### Shu Kawaguchi

On the ranks of the $2$-Selmer groups of twists of a given elliptic curve
1253–1279