BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Junyi Xie (CNRS Rennes) DTSTART:20201229T013000Z DTEND:20201229T023000Z DTSTAMP:20260423T024027Z UID:iccm2020/98 DESCRIPTION:Title: On the Zariski dense orbit conjecture\nby Junyi Xie (CNRS Rennes) as part of ICCM 2020\n\n\nAbstract\nWe prove the following theorem. Let f be a dominant endomorphism of a projective surface over an algebraically clo sed field of characteristic 0. If there is no nonconstant invariant ration al function under f\, then there exists a closed point whose orbit under f is Zariski dense. This result gives us a positive answer to the Zariski d ense orbit conjecture for endomorphisms of projective surfaces. We define a new canonical topology on varieties over an algebraically closed field w hich has finite transcendence degree over Q. We call it the adelic topolog y. This topology is stronger than the Zariski topology and an irreducible variety is still irreducible in this topology. Using the adelic topology\, we propose an adelic version of the Zariski dense orbit conjecture\, whic h is stronger than the original one and quantifies how many such orbits th ere are. We also prove this adelic version for endomorphisms of projective surfaces\, for endomorphisms of abelian varieties\, and split polynomial maps. This yields new proofs of the original conjecture in the latter two cases.\n LOCATION:https://researchseminars.org/talk/iccm2020/98/ END:VEVENT END:VCALENDAR