## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics.

A tameness criterion for Galois representations associated to modular forms $(\mod p)$Volume 61, Number 2 (1990)
K-theory and derived equivalencesVolume 124, Number 3 (2004)
Irreducible modular representations of $\mathrm{GL}_2$ of a local fieldVolume 75, Number 2 (1994)
Trilinear forms and the central values of triple product $L$ -functionsVolume 145, Number 2 (2008)
Schur multipliersVolume 44, Number 3 (1977)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935 --
• Access: By subscription only
• Euclid URL: http://projecteuclid.org/dmj

### Featured article

#### Symmetric differentials and the fundamental group

Volume 162, Number 14
##### Abstract

We show that any smooth complex projective variety whose fundamental group has a complex representation with infinite image must have a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). Along the way, we produce many symmetric differentials on the base of a variation of Hodge structures.