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- W2949355959 abstract "Let $M in M_n (mathbb Z)$ denote any matrix. Thinking of $M$ as a linear map $M:{mathbb Z}^n to {mathbb Z}^n$, we denote by ${Image}(M)$ the $mathbb Z$-span of the column vectors of $M$. Let $e_1, ..., e_n,$ denote the standard basis of ${mathbb Z}^n$, and let $E_{ij}: = e_i - e_j$, $ (i neq j)$. In this article, we are interested in the group ${mathbb Z}^n /{Image}(M)$, and in particular in the elements of this group defined by the images $tau_{ij}$ of the vectors $E_{ij}$ under the quotient ${mathbb Z}^n to {mathbb Z}^n / {Image} (M)$. Most of this article is devoted to the study of the case where $M$ is the laplacian of a graph. In this case, the elements $tau_{ij}$ have finite order, and we study how the geometry of the graph relates to these orders. Applications to the theory of semistable reduction of curves will appear in a forthcoming article." @default.
- W2949355959 created "2019-06-27" @default.
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- W2949355959 date "1999-03-18" @default.
- W2949355959 modified "2023-09-27" @default.
- W2949355959 title "Arithmetical properties of Laplacians of graphs" @default.
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