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