Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 54, Number 1

#### Publication Date: 1987

Yuri Ivanovich Manin

I. R. Shafarevich; ii-iii

Cycles, curves and vector bundles on an algebraic surface

A. N. Tyurin; 1-26

On the homology of Poisson algebra of odd variables

O. Ogievetsky; 27-40

On the monodromy groups attached to certain families of exponential sums

Nicholas M. Katz; 41-56

A note on pseudo-CM representations and differential Galois groups

Nicholas M. Katz and Richard Pink; 57-65

Representation theory and the cuspidal group of $X(p)$

Benedict H. Gross; 67-75

A functional equation of the non-Archimedian Rankin convolution

A. A. Panchishkin; 77-89

Stable bundles and integrable systems

Nigel Hitchin; 91-114

Exceptional vector bundles on projective spaces

A. L. Gorodentsev and A. N. Rudakov; 115-130

Endomorphisms and torsion of abelian varieties

Yu. G. Zarhin; 131-145

Constructive high-dimensional sphere packings

S. N. Litsyn and M. A. Tsfasman; 147-161

Another proof of a conjecture of S. P. Novikov on periods of abelian integrals on Riemann surfaces

Enrico Arbarello and Corrado De Concini; 163-178

Sur les représentations modulaires de degré $2$ de $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})$

Jean-Pierre Serre; 179-230

Infinite determinants, stable bundles and curvature

S. K. Donaldson; 231-247

$p$-adic $K$-theory of elliptic curves

Christophe Soulé; 249-269