Extending Self-Maps to Projective Space over Finite Fields
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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 P[superscript n] over a field, and φ: X → X satisfies φ∗O[subscript X](1) [~ over _] O[subscript X](d) for some d ≥ 2, then there exists r ≥ 1 such that φ[superscript r] extends to a morphism P[superscript n] → P[superscript n].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
European Math Society
Poonen, Bjorn. "Extending Self-Maps to Projective Space over Finite Fields." Documenta Mathematica 18 (2013), 1039-1044.
Author's final manuscript