2025/04/21 by Oh, Gyujin, Shimizu, Koji
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2504.14801
Given a liftable smooth proper variety over \mathbbFp, we construct the moduli stacks of crystals and isocrystals on it. We show that the former is a formal algebraic stack over ℤp and the latter is an adic stack -- Artin stack in rigid geometry -- over ℚp. Both stacks come equipped with the Verschiebung endomorphism V corresponding to the Frobenius pullback of (iso)crystals. We study the geometry of the V-fixed points over the open substack of irreducible isocrystals, which we use to geometrically count the rank one F-isocrystals. Along the way, we carefully develop the theory of adic stacks.