188 research outputs found
The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves
We study the intersection of two particular Fermat hypersurfaces in
over a finite field. Using the Kani-Rosen decomposition we study
arithmetic properties of this curve in terms of its quotients. Explicit
computation of the quotients is done using a Gr\"obner basis algorithm. We also
study the -rank, zeta function, and number of rational points, of the modulo
reduction of the curve. We show that the Jacobian of the genus 2 quotient
is -split
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