400 research outputs found
Duality of Anderson -motives having
This paper extends the main result of the paper "Duality of Anderson
-motives", that the lattice of the dual of a t-motive is the dual
lattice of , to the case when the nilpotent operator of is non-zero.Comment: 21 pages; minor correction
Lattice map for Anderson t-motives : first approach
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 close to 1 -- 1. Namely, let
be a t-motive of dimension and rank \ --- \ the -th power of the
Carlitz module of rank 2, and let be a t-motive which is in some sense
"close" to . We consider the lattice map , where
is a lattice in . We show that the lattice map is an isomorphism in a
"neighborhood" of . 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.Comment: 26 pages. Minor improvement
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