Geodesic
Extending self-maps to projective space over finite fields
Documenta mathematica, Tome 18 (2013), pp. 1039-1044
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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 Pn over a field, and φ:X→X satisfies φ∗OX​(1)≃OX​(d) for some d≥2, then there exists r≥1 such that φr extends to a morphism Pn→Pn.
DOI : 10.4171/dm/420
Classification : 37P25, 37P55
Mots-clés : self-map, closed point sieve 
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     author = {Bjorn Poonen},
     title = {Extending self-maps to projective space over finite fields},
     journal = {Documenta mathematica},
     pages = {1039--1044},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/420},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/420/}
}
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Bjorn Poonen. Extending self-maps to projective space over finite fields. Documenta mathematica, Tome 18 (2013), pp. 1039-1044. doi: 10.4171/dm/420

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