2010/12/13 by Mircea Mustaţă, Mircea Mustata, Mustata, Mircea
Computer Science · Mathematics · #14F30) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary (13A35) #math.AC #math.AG #secondary (14F18
paper · pdf · doi:10.48550/arxiv.1012.2915
7 pages; v.2: minor changes, to appear in Proc. Amer. Math. Soc
openalex publication_date 2010/12/13 · arxiv created 2011/06/01 · arxiv updated 2011/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the following conjecture: if X is a smooth projective variety over a field of characteristic zero, then there is a dense set of reductions Xs to positive characteristic such that the action of the Frobenius morphism on the top Zariski cohomology of the structure sheaf on Xs is bijective. We also consider the conjecture relating the multiplier ideals of an ideal J on a nonsingular variety in characteristic zero, and the test ideals of the reductions of J to positive characteristic. We prove that the latter conjecture implies the former one. The converse was proved in a joint paper of the author with V. Srinivas.