Geodesic
Extending self-maps to projective space over finite fields
Documenta mathematica, Tome 18 (2013), pp. 1039-1044.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using the closed point sieve, we extend to finite fields the following theorem proved by A. Bhatnagar and L. Szpiro over infinite fields: if $X$ is a closed subscheme of $\{P}^n$ over a field, and $\phi \colon X \to X$ satisfies $\phi^* \mathscr{O}_X(1) \isom \mathscr{O}_X(d)$ for some $d \ge 2$, then there exists $r \ge 1$ such that $\phi^r$ extends to a morphism $\{P}^n \to \{P}^n$.
Classification : 37P25, 37P55
Keywords: self-map, closed point sieve 
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     author = {Poonen, Bjorn},
     title = {Extending self-maps to projective space over finite fields},
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Poonen, Bjorn. Extending self-maps to projective space over finite fields. Documenta mathematica, Tome 18 (2013), pp. 1039-1044. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a18/