The asymptotic behavior of automorphism groups of function fields over finite fields
摘要：This talk is to investigate the asymptotic behavior of automorphism groups of function fields when genus tends to infinity. Motivated by applications in coding and cryptography, we consider the maximum size of abelian subgroups of the automorphism group $\Aut(F/\F_q)$ in terms of genus g_F for a function field F over a finite field F_q. The asymptotic behavior of the maximum size m_F is investigated by defining $M_q=\limsup_{g_F\rightarrow\infty}\frac{m_F \cdot \log_q m_F}{g_F}$, where F runs through all function fields over F_q. It turns out that $2\le M_q\le 4$ and m_F grows much more slowly than genus does asymptotically. The second part of this talk is to study the maximum size b_F of subgroups of automorphism groups whose order is coprime to q. The asymptotic behavior of $b_F$ is investigated by defining $B_q=\limsup_{g_F\rightarrow\infty}\frac{b_F}{g_F}$, where F runs through all function fields over F_q. A lower bound is provided by explicitly constructing some tame towers of function fields.
报告地点：扬州大学数学科学学院38号楼报告厅
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