The Cartier–Witt divisor description conjecture for cwidehat\bbF1Syncwidehat{\bbF}_1^\mathrm{Syn}

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Let \bbS\mathbblΔ^\bbS^{\widehat{\mathbbl{\Delta}}} be the complement of the zero section in the universal formal group \bbG^univ=\bbS\calN^\widehat{\bbG}_\mathrm{univ}=\bbS^{\widehat{\calN}}. For a pp-nilpotent ring RR, consider the pullback

Spec⁡R×\calMfg\bbS\mathbblΔ^.\operatorname{Spec}R\times_{\calM_\mathrm{fg}}\bbS^{\widehat{\mathbbl{\Delta}}}.

Cartier–Witt divisor conjecture. An RR-point of \bbF^1Syn\widehat{\bbF}_1^\mathrm{Syn} is given by a formal group over RR, a Cartier–Witt divisor on this pullback, and an isomorphism over the pullback between the given formal group and the Drinfeld formal group, compatible with their natural sections. The statement assumes a reasonable theory of Cartier–Witt divisors on the relevant stacks and uses the specified section of the Drinfeld formal group.

References

Primary source

Dhilan Lahoti and Deven Manam, “Cohomology theories in the moduli of ring stacks”, arXiv:2510.09582 (2025).

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