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- W2951614665 abstract "There exists a lattice map from the set of pure uniformizable Anderson t-motives to the set of lattices. It is not known what is the image and the fibers of this map. We prove a local result that sheds the first light to this problem and suggests that maybe this map is to 1 -- 1. Namely, let $M(0)$ be a t-motive of dimension $n$ and rank $r=2n$ --- the $n$-th power of the Carlitz module of rank 2, and let $M$ be a t-motive which is in some sense close to $M(0)$. We consider the lattice map $M mapsto L(M)$, where $L(M)$ is a lattice in $C^n$. We show that the lattice map is an isomorphism in a neighborhood of $M(0)$. Namely, we compare the action of monodromy groups: (a) from the set of equations defining t-motives to the set of t-motives themselves, and (b) from the set of Siegel matrices to the set of lattices. The result of the present paper gives that the size of a neighborhood, where we have an isomorphism, depends on an element of the monodromy group. We do not know whether there exists a universal neighborhood. Method of the proof: explicit solution of an equation describing an isomorphism between two t-motives by a method of successive approximations using a version of the Hensel lemma." @default.
- W2951614665 created "2019-06-27" @default.
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- W2951614665 date "2011-09-04" @default.
- W2951614665 modified "2023-09-27" @default.
- W2951614665 title "Lattice map for Anderson T-motives: first approach" @default.
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