Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds

2023/09/07 by Chmiel, Tymoteusz, Oczko, Marcin
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.04008

Abstract

For any prime p>5 we construct a Calabi-Yau threefold X defined over a finite extension K of ℚ_p such that every model of X over SpecO_K has singular special fiber, yet the Galois action on the ℓ-adic cohomology group H³_\acuteet(X,ℚ_ℓ) is unramified for ℓ≠ p and crystalline for ℓ=p. This provides a counterexample to the analogue of the Néron-Ogg-Shafarevich criterion for three-dimensional Calabi-Yau manifolds.

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