On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.

Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.

Groups of Order 32 as Galois Groups

2000 Mathematics Subject Classification: 12F12.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.

Some new Results for Additive Self-Dual Codes over GF(4)

* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Quaternion Extensions of Order 16

2000 Mathematics Subject Classification: 12F12