English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

Motivated by Lang–Vojta’s conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any given number field is finite by combining Amerik’s theorem for dynamical systems of infinite order with properties of Prokhorov–Shramov’s notion of quasi-minimal models. We also prove a similar result in the geometric setting by using again not only Amerik’s theorem and Prokhorov–Shramov’s notion of quasi-minimal model but also Weil’s regularization theorem for birational self-maps and properties of dynamical degrees. Furthermore, in the geometric setting, we obtain an analogue of Kobayashi–Ochiai’s finiteness result for varieties of general type and thereby generalize Noguchi’s theorem (formerly Lang’s conjecture).

Finiteness Properties of Pseudo-Hyperbolic Varieties