Generic vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties

DOI10.1353/ajm.2016.0031zbMath1408.14073arXiv1310.2996OpenAlexW1821847917MaRDI QIDQ2816469

Zsolt Patakfalvi, Christopher Derek Hacon

Publication date: 22 August 2016

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2996

Mathematics Subject Classification ID

Vanishing theorems in algebraic geometry (14F17) Algebraic theory of abelian varieties (14K05) Positive characteristic ground fields in algebraic geometry (14G17)

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Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers ⋮ A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf ⋮ Generic vanishing in characteristic \(p>0\) and the geometry of theta divisors ⋮ Globally \(+\)-regular varieties and the minimal model program for threefolds in mixed characteristic ⋮ Generic vanishing and classification of irregular surfaces in positive characteristics ⋮ Abundance for 3-folds with non-trivial Albanese maps in positive characteristic ⋮ Theta divisors whose Gauss map has a fiber of positive dimension ⋮ On the abundance problem for 3-folds in characteristic \(p>5\) ⋮ When is the Albanese morphism an algebraic fiber space in positive characteristic? ⋮ Positive characteristic algebraic geometry ⋮ Birational characterization of abelian varieties and ordinary abelian varieties in characteristic \(p>0\) ⋮ On the characterization of abelian varieties for log pairs in zero and positive characteristic

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