Extending Self-Maps to Projective Space over Finite Fields
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 ex...
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| Format: | Article |
| Language: | en_US |
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European Math Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/93177 https://orcid.org/0000-0002-8593-2792 |
| 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[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]. |
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