2018/12/30 by A. Grishkov, Grishkov, A., Dmitry Logachev +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.1812.11576
Let M be an uniformizable Anderson t-motive of rank r, L its lattice and l_*:=\l1,…, lr\ its basis. We define a map δ from the set of these bases to a flag variety (the present text gives the definition of δ only for elements of the maximal Schubert cell, and for few other cases). If l_* belongs to the maximal Schubert cell then δ(l_*) is described as a set of matrices parametrized by integer points of a tetrahedron; they are called the Siegel element of l_*. We give explicit formulas for a Siegel element for M' -- the dual of M. As a by-product, we get another proof of the theorem that the lattice of M' is the dual of the lattice of M, independent of the proof obtained by U. Hartl and A.-K. Juschka. Generalizations of this result to non-maximal Schubert cells, other tensor operations (tensor product and Hom) and t-motives having non-trivial endomorphism rings, are subjects of further research.