The tilting property for F_*^e\mathcal O_X on Fano surfaces and threefolds

2024/05/23 by Mallory, Devlin
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.14070

Abstract

Let X be a smooth variety over a field of characteristic p. It is a natural question whether the Frobenius pushforwards F_*^e\mathcal O_X of the structure sheaf are tilting bundles. We show if X is a smooth del Pezzo surface of degree ≤ 3 or a Fano threefold with vol(K_X)<24 over a field of characteristic p, then Extⁱ(F_*^e\mathcal O_X,F^e_*\mathcal O_X)≠ 0 and thus F_*^e\mathcal O_X is not tilting.

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