2012/12/14 by Emmanuel Hallouin, Hallouin, Emmanuel, Marc Perret +1
Mathematics · #11G20 #14G05 #14G15 #14H20 #5C38 #5C50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Spectral Theory in Mathematical Physics #math.AG #math.NT #msc:11G20 #msc:14G05 #msc:14G15 #msc:14H20 #msc:5C38 #msc:5C50
paper · pdf · doi:10.48550/arxiv.1212.3465
31 pages, 3 figures
openalex publication_date 2012/12/14 · arxiv created 2014/03/18 · arxiv updated 2014/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new way to study recursive towers of curves over a finite field, defined from a bottom curve \Cun and a correspondence \Cdeux on \Cun.In particular, we study their asymptotic behavior. A close examination of singularities leads to a necessary condition for a tower to be asymptotically good. Then, spectral theory on a directed graph and considerations on the class of \Cdeux in \NS (\Cun × \Cun) lead to the fact that, under some mild assumptions, a recursive tower which does not reach Drinfeld-Vladut bound cannot be optimal in Tsfasmann-Vladut sense. Results are applied to the Bezerra-Garcia-Stichtenoth tower along the paper for illustration.