Extending Self-maps to Projective Space over Finite Fields
نویسنده
چکیده
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 over a field, and φ : X → X satisfies φOX(1) ' OX(d) for some d ≥ 2, then there exists r ≥ 1 such that φ extends to a morphism P → P.
منابع مشابه
Extending Self-maps to Projective Space
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 over a field, and φ : X → X satisfies φOX(1) ' OX(d) for some d ≥ 2, then there exists r ≥ 1 such that φ extends to a morphism P → P.
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