arXiv subjects

Julie Tavernier

Publications and source records attributed to Julie Tavernier.

3 recordsLinked to original sources

arXiv2026

The McKay correspondence and local heights for wild-by-tame split metacyclic groups

We study the McKay correspondence for the representations of certain wild-by-tame split metacyclic groups whose order is divisible by the characteristic of the base field. We calculate the stringy motive of the quotient variety and find a formula for its stringy Euler number. As a consequence, we prove that a crepant resolution of the quotient variety (provided one exists) does not in general have Euler characteristic equal to the number of conjugacy classes in $G$, in contrast to the classical case. In particular, we show it depends on the choice of representation as well as the group. As part of this, we compute the v-function associated to a $G$-representation, corresponding to a stacky local height function.

math.AG↗

arXiv2025

Counting abelian number fields with restricted ramification type

We count abelian number fields ordered by arbitrary height function whose generator of tame inertia is restricted to lie in a given subset of the Galois group, and find an explicit formula for the leading constant. We interpret our results as a version of the Batyrev-Manin conjecture on $BG$ and rephrase our result on number fields with restricted ramification type in terms of integral points on $BG$. We also prove that such number fields are equidistributed with respect to suitable collections of infinitely many local conditions.

math.NT↗

arXiv2024

Abelian number fields with frobenian conditions

We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular we find an asymptotic for the number of abelian field extensions of a number field k whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.

math.NT↗