The paper proves an equivalence between Cartier crystals and V-crystals on dual abelian varieties and derives H^0(X,ω_X)≠0, with S^0(X,ω_X)≠0 in the ordinary case, for normal proper varieties of maximal Albanese dimension.
On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that a smooth proper weakly ordinary variety $X$ of maximal Albanese dimension satisfies $\chi(X, \omega_X) \geq 0$. We also show that if $X$ is not of general type, then $\chi(X, \omega_X) = 0$ and the Albanese image of $X$ is fibered by abelian varieties. The proof uses the positive characteristic generic vanishing theory developed by Hacon-Patakfalvi, as well as our recent Witt vector version of Grauert-Riemenschneider vanishing.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Generic vanishing theory in positive characteristic
The paper proves an equivalence between Cartier crystals and V-crystals on dual abelian varieties and derives H^0(X,ω_X)≠0, with S^0(X,ω_X)≠0 in the ordinary case, for normal proper varieties of maximal Albanese dimension.