EuDML | Browse

We study a moduli space ${𝒜𝒮}_{g}$ for Artin-Schreier curves of genus $g$ over an algebraically closed field $k$ of characteristic $p$ . We study the stratification of ${𝒜𝒮}_{g}$ by $p$ -rank into strata ${𝒜𝒮}_{g . s}$ of Artin-Schreier curves of genus $g$ with $p$ -rank exactly $s$ . We enumerate the irreducible components of ${𝒜𝒮}_{g, s}$ and find their dimensions. As an application, when $p = 2$ , we prove that every irreducible component of the moduli space of hyperelliptic $k$ -curves with genus $g$ and $2$ -rank $s$ has dimension $g - 1 + s$ . We also determine all pairs $(p, g)$ for...

Displaying 1 – 9 of 9

The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer

The constant term of the cubic theta series.

The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer.

The field of moduli of abelian surfaces with complex multiplication.

The $p$ -rank stratification of Artin-Schreier curves

The periods of abelian varieties with complex multiplication and the spectral values of certain zeta functions

The Tate conjecture for certain abelian varieties over finite fields

Torsion points on abelian varieties of CM-type

Travaux de Shimura et Taniyama sur la multiplication complexe

Currently displaying 1 – 9 of 9