1. CJM 2004 (vol 56 pp. 612)
 Pál, Ambrus

Solvable Points on Projective Algebraic Curves
We examine the problem of finding rational points defined over
solvable extensions on algebraic curves defined over general fields.
We construct nonsingular, geometrically irreducible projective curves
without solvable points of genus $g$, when $g$ is at least $40$, over
fields of arbitrary characteristic. We prove that every smooth,
geometrically irreducible projective curve of genus $0$, $2$, $3$ or
$4$ defined over any field has a solvable point. Finally we prove
that every genus $1$ curve defined over a local field of
characteristic zero with residue field of characteristic $p$ has a
divisor of degree prime to $6p$ defined over a solvable extension.
Categories:14H25, 11D88 

2. CJM 2003 (vol 55 pp. 331)
 Savitt, David

The Maximum Number of Points on a Curve of Genus $4$ over $\mathbb{F}_8$ is $25$
We prove that the maximum number of rational points on a smooth,
geometrically irreducible genus 4 curve over the field of 8 elements
is 25. The body of the paper shows that 27 points is not possible by
combining techniques from algebraic geometry with a computer
verification. The appendix shows that 26 points is not possible by
examining the zeta functions.
Categories:11G20, 14H25 
