Thursday 23 Nov 2017Maximal quartic orders with small Galois group and monogenic cubic resolvent

Dr. Stanley Xiao - University of Oxford

H103 14:30-16:30


In this talk we give an overview of current work with C. Tsang on maximal quartic orders with small Galois group and monogenic cubic resolvent. In particular, we give necessary and sufficient conditions for a quartic order with small Galois group and monogenic cubic resolvent, or equivalently, the \operatorname{GL}_2(\mathbb{Z})-equivalence class of an integral binary quartic form, to form a maximal order. We will then show how to count such objects ordered by a suitable Artin conductor. This builds upon a recent paper of Altug, Shankar, Varma, and Wilson and on earlier works of Bhargava and Wood. 


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