The toric regulator and Sreekantan regulator comparison conjecture

Let XX be a variety with completely degenerate reduction, and let \ell be a prime. The toric regulator at \ell is obtained from the étale regulator by passage to the relevant toric quotient, while the Sreekantan regulator is the boundary map

\hmot(X,k+1,r)CHr(X,2rk1)CHr1(Y,2rk2)Q.\hmot(X,k+1,r)\cong CH^r(X,2r-k-1)\xrightarrow{\partial}CH^{r-1}(Y,2r-k-2)\otimes {\mathbb Q}.

Toric–Sreekantan regulator conjecture. For each prime \ell, the valuation of the toric regulator at \ell is the Sreekantan regulator tensored with Q{\mathbb Q}_\ell. This conjecture predicts compatibility between the toric regulator constructed from the étale regulator and Sreekantan's regulator in the function-field setting. The supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Amnon Besser, “Regulators and derivatives of Vologodsky functions with respect to log(p)”, arXiv:2502.16738 (2025).

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