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- W2072940964 abstract "Abstract We give a method to describe the quotient of the local Bruhat–Tits tree T P for PGL 2 ( K ) , where K is a global function field, by certain subgroups of PGL 2 ( K ) of arithmetical significance. In particular, we can compute the quotient of T P by an arithmetic subgroup PGL 2 ( A ) , where A = A P is the ring of functions that are regular outside P, recursively for a place P of any degree, when K is a rational function field. We achieve this by proving that the infinite matrices whose coordinates are the numbers of neighbors of a vertex in T P corresponding to orders in a fixed isomorphism class commute for different places P, using tools from the theory of representations of orders. The latter result holds for every global function field K." @default.
- W2072940964 created "2016-06-24" @default.
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- W2072940964 date "2014-03-01" @default.
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- W2072940964 title "Computing quaternion quotient graphs via representations of orders" @default.
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- W2072940964 doi "https://doi.org/10.1016/j.jalgebra.2013.12.015" @default.
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