Equality with the crystalline Hyodo–Kato map

Determine whether the rationalization of the integral comparison map equals the crystalline Hyodo–Kato map, up to Frobenius twist, and prove this equality if it holds.

Background

The paper defines an integral comparison map between log crystalline cohomology over the hollow log base and the corresponding de Rham-side object. Its rationalization can be compared with the crystalline Hyodo–Kato map constructed by Ertl and Yamada.

The authors explain that a positive answer would imply the compatibility asked for in the preceding question. In the ramified case, the Tate-curve example indicates that a Frobenius twist, represented by a suitable power of the linearized crystalline Frobenius, must be incorporated.

References

Is it true that $\Phi{\rm rat}{\pi, \mathfrak X}=\Psi{\rm crys}{\pi, \mathfrak X}$, up to Frobenius twist?

— An integral Hyodo--Kato isomorphism  (2609.00723 - Binda et al., 1 Sep 2026) in Section 1, subsection “Questions and related works,” second Question

Another reasonable question is whether an analogue of Theorem~\ref{thm:intro-integralHK} for coefficients holds or not. The most natural formulation of the question is in terms of logarithmic prismatic crystals, and a positive answer would give an integral refinement to the transfer Theorem of Ogus .

— An integral Hyodo--Kato isomorphism  (2609.00723 - Binda et al., 1 Sep 2026) in Section 1, subsection “Questions and related works,” paragraph following the comparison diagram