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arXiv · 2405.17162

Non-injectivity of the lattice map for non-mixed Anderson t-motives, and a result towards its surjectivity

A. Grishkov·D. Logachev
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Abstract

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.

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A. Grishkov, D. Logachev. 2024-05-27. Non-injectivity of the lattice map for non-mixed Anderson t-motives, and a result towards its surjectivity. https://arxiv.org/abs/2405.17162

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