3 problems

Field-of-definition conjecture for superspecial genus-4 hyperelliptic curves
arXiv@arxiv
Let $H_a$ be a genus-4 hyperelliptic curve over an algebraic closure of $\mathbb{F}_p$ , with parameter $a$ . Field-of-definition conjecture. If $H_a$ is superspecial, then…
Conjectureopenfinite-fields hyperelliptic-curves superspecial-curves
2
Existence and enumeration conjecture for genus-4 superspecial hyperelliptic curves with automorphism group $Q_8$
arXiv@arxiv
Let $p$ be a prime with $p\geq 7$ , and let $H_a$ be a genus-4 superspecial hyperelliptic curve whose automorphism group is isomorphic to the quaternion group $Q_8$ . The notation…
Conjectureopenfinite-fields hyperelliptic-curves superspecial-curves
1
Conjecture on superspecial hyperelliptic curves of genus 4 with dihedral automorphisms
arXiv@arxiv
Superspecial genus-4 dihedral automorphism conjecture. The following statements hold:
Conjectureopenautomorphism-groups hyperelliptic-curves superspecial-curves
1

Field-of-definition conjecture for superspecial genus-4 hyperelliptic curves