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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17162 |
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| _version_ | 1866910575541354496 |
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| author | Grishkov, A. Logachev, D. |
| author_facet | Grishkov, A. Logachev, D. |
| contents | Let $M$ be an uniformizable Anderson t-motive and $L(M)$ its lattice. First, we prove by an explicit construction that for the non-mixed $M$ the lattice map $M\mapsto L(M)$ is not injective. Second, we show that some lattices which do not belong to the set $L(M)$ of pure $M$, are lattices of non-pure $M$. This is a result towards surjectivity of the lattice map. The t-motives used in the proofs are non-pure t-motives of dimension 2, rank 3. Finally, we start calculations in order to answer a question whether all these t-motives are uniformizable, or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-injectivity of the lattice map for non-mixed Anderson t-motives, and a result towards its surjectivity Grishkov, A. Logachev, D. Number Theory 11G09 Let $M$ be an uniformizable Anderson t-motive and $L(M)$ its lattice. First, we prove by an explicit construction that for the non-mixed $M$ the lattice map $M\mapsto L(M)$ is not injective. Second, we show that some lattices which do not belong to the set $L(M)$ of pure $M$, are lattices of non-pure $M$. This is a result towards surjectivity of the lattice map. The t-motives used in the proofs are non-pure t-motives of dimension 2, rank 3. Finally, we start calculations in order to answer a question whether all these t-motives are uniformizable, or not. |
| title | Non-injectivity of the lattice map for non-mixed Anderson t-motives, and a result towards its surjectivity |
| topic | Number Theory 11G09 |
| url | https://arxiv.org/abs/2405.17162 |