Sebastian Monnet

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20222025

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math.NT2025

Explicit bounds on the transcendental Brauer group of K3 surfaces with principal complex multiplication

Sebastian Monnet

Let $X$ be a K3 surface defined over a number field $k$ , with principal complex multiplication by a CM field $E$ . We find explicit bounds, in terms of $k$ and $E$ , on the size of t…

math.NT2024

$S_{n}$ -extensions with prescribed norms

Sebastian Monnet

Given a number field $k$ , a finitely generated subgroup $A \subseteq k^{\times}$ , and an integer $n \geq 3$ , we study the distribution of $S_{n}$ -extensions of $k$ such that th…

math.NT2023

Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

Sebastian Monnet

Given a $2$ -adic field $K$ , we give formulae for the number of totally ramified quartic field extensions $L / K$ with a given discriminant valuation and Galois closure group. We use…

math.NT2022

$S_{4}$ -quartics with Prescribed Norms

Sebastian Monnet

Given a number field $k$ and a finitely generated subgroup $A \subseteq k^{*}$ , we study the distribution of $S_{4}$ -quartic extensions of $k$ such that the elements of $\mat…

Explicit bounds on the transcendental Brauer group of K3 surfaces with principal complex multiplication

Sn​-extensions with prescribed norms

Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

S4​-quartics with Prescribed Norms

$S_{n}$ -extensions with prescribed norms

$S_{4}$ -quartics with Prescribed Norms