Rational points on log Fano threefolds over a finite field

Abstract

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano threefold over a finite field has a rational point.

35 pages, v2: minor revisions, v3: minor revisions, to appear in Journal of the European Mathematical Society

References in corpus (3)

• Behavior of canonical divisors under purely inseparable base changes
• Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field
• On relative rational chain connectedness of threefolds with anti-big canonical divisors in positive characteristics

Cited by in corpus (4)

• Minimal model program for log canonical threefolds in positive characteristic
• Non-normal purely log terminal centres in characteristic $p\ge 3$
• Discrepancies of $p$-cyclic quotient varieties
• Congruences of the cardinalities of rational points of log Fano varieties and log Calabi-Yau varieties over the log points of finite fields