Description
Online Number Theory Seminar
Abstract: A degree $d$ homogeneous form $f(x,y)$ determines a ring of rank $d$ over $Z,$ the ring of functions on the scheme $\{(x,y) : f(x,y) = 0\}.$ For $d < 4,$ this construction recovers all rings of integers of number fields of degree $d.$ For $d = 4,$ we show that a positive proportion of quartic ring of integers do not arise this way. I'll motivate this question a bit and then explain the proof. This is joint work with Levent Alpoge and Manjul Bhargava.
For access please contact the organizers (ntrg[at]science.unideb.hu).