3 problems

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Radicality conjecture for the Hasse–Witt ideal of genus-4 double covers
At least 11 years old
Radicality conjecture. The ideal $I_M$ is radical for every prime $p\geq 5$ .
openalgebraic-geometry hasse-witt-matrices superspecial-curves
012
Field-of-definition conjecture for superspecial genus-4 hyperelliptic curves
About 1 year old
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…
openfinite-fields hyperelliptic-curves superspecial-curves
013
Conjecture on superspecial hyperelliptic curves of genus 4 with dihedral automorphisms
About 3 years old
Superspecial genus-4 dihedral automorphism conjecture. The following statements hold:
openautomorphism-groups hyperelliptic-curves superspecial-curves
013

Radicality conjecture for the Hasse–Witt ideal of genus-4 double covers