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I am interested in Richelot isogenies between ordinary abelian surfaces in characteristic $2$. If I am not mistaken, the corresponding theory is developed in Article "J.-B. Bost, J.-F. Mestre, Moyenne arithmético-géométrique et périodes des courbes de genre 1 et 2". Unfortunately, this article is not available in Internet. Since it was published a long time ago (in 1988), I guess, it can be freely distributed. I would be very grateful if you provided me the mentioned article or another relevant source.

Thanks in advance.

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  • $\begingroup$ Bost & Mestre work over the reals, and do not develop the characteristic 2 case. Brock and Howe is a very good reference for Richelot isogenies in characteristic 2. $\endgroup$
    – Ben Smith
    Commented Jun 15, 2021 at 12:54
  • $\begingroup$ Brock and Howe consider the supersingular case. Do you think, their results can be generalized to the ordinary case without problems ? $\endgroup$
    – Dimitri Koshelev
    Commented Jun 16, 2021 at 9:40
  • $\begingroup$ The main results of Brock & Howe are indeed for the supersingular case, but the background in the introduction covers the ordinary case. $\endgroup$
    – Ben Smith
    Commented Jun 17, 2021 at 11:42
  • $\begingroup$ For the ordinary case in the introduction they propose to use the theory of canonical lifts. For example, given two ordinary elliptic curves $E_0$, $E_1$ over a finite field $\mathbb{F}_{q}$ of characteristic $2$, is it possible to deduce explicit formulas of 2-sheeted covers from a genus 2 curve to these elliptic curves as in the article of Howe, Leprévost, Poonen ? For fixed $E_0$, $E_1$, $q$ we can apply Satoh algorithm in order to find the canonical lifts of the elliptic curves. But I am not sure that we can do this in general (when the parameters are variable). $\endgroup$
    – Dimitri Koshelev
    Commented Jun 17, 2021 at 16:10

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