Leírás
Online Number Theory Seminar
Abstract: A number field $K$ is $\textit{monogenic}$ over $\mathbb{Q}$ if the ring of integers admits a power integral basis, i.e., a $\mathbb{Z}$-basis of the form $\{1, \alpha, \alpha^2,\dots, \alpha^{n-1}\}$. In this case we call $\alpha$ a $\textit{monogenerator}$.
The first portion of the talk will be spent covering classical examples and foundational results. The latter part of the talk will be devoted to recent work constructing a general "moduli space" of monogenerators. Specifically, given an extension of algebras $B/A$, we construct a $\textit{scheme}$ $\mathcal{M}_{B/A}$ parameterizing the possible choices of a monogenerator for $B$ over $A$.
For access please contact the organizers (ntrg[at]science.unideb.hu).