On ramification and genus of recursive towers.
Galois towers over non-prime finite fields
We construct Galois towers with good asymptotic properties over any non-prime finite field ; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over of increasing genus, such that all the extensions are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties...
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