Explicit endomorphism of the Jacobian of a hyperelliptic function field   of genus 2 using base field operations
  We present an efficient endomorphism for the Jacobian of a curve $C$ of genus 2 (hyperelliptic) for divisors having a Non disjoint support. This extends the work of Costello and Lauter in [12] who calculated explicit formulae for divisor doubling and addition of divisors with disjoint support in $\mathbb{J}(C)$ using only base field operations. Explicit formulae is presented for this third case and a slightly different approach for divisor doubling. 
Eduardo Ruiz Duarte, Octavio P\'aez Osuna
math.AG cs.CR