Algebraic types in Zilber's exponential field
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909461999779840 |
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| author | Aslanyan, Vahagn Kirby, Jonathan |
| author_facet | Aslanyan, Vahagn Kirby, Jonathan |
| contents | We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic types in Zilber's exponential field Aslanyan, Vahagn Kirby, Jonathan Logic Number Theory 03C60 (primary), 03C65, 12L12 We characterise the model-theoretic algebraic closure in Zilber's exponential field. A key step involves showing that certain algebraic varieties have finite intersections with certain finite-rank subgroups of the graph of exponentiation. Mordell-Lang for algebraic tori (a theorem of Laurent) plays a central role in our proof. |
| title | Algebraic types in Zilber's exponential field |
| topic | Logic Number Theory 03C60 (primary), 03C65, 12L12 |
| url | https://arxiv.org/abs/2405.01399 |