Rachel Davis

activity

20142025

most citedCohomology groups of Fermat curves via ray class fields of cyclotomic fields

1 citations · 1 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2025

Hypergeometric decomposition of Delsarte K3 pencils

Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro +4

We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeomet…

math.NT2018

The Galois action on the lower central series of the fundamental group of the Fermat curve

Rachel Davis, Rachel Pries, Kirsten Wickelgren

Information about the absolute Galois group $G_{K}$ of a number field $K$ is encoded in how it acts on the étale fundamental group $π$ of a curve $X$ defined over $K$ . In the case th…

math.NT2018★ 1 cited

Cohomology groups of Fermat curves via ray class fields of cyclotomic fields

Rachel Davis, Rachel Pries

The absolute Galois group of the cyclotomic field $K = Q (ζ_{p})$ acts on the étale homology of the Fermat curve $X$ of exponent $p$ . We study a Galois cohomology group which…

math.NT2018

Arithmetic of quaternion origami

Rachel Davis, Edray Herber Goins

We study origami $f : C \to E$ with $G$ -Galois cover $Q_{8}$ . For a point $P \in E (Q) \ {O}$ , we study the field obtained by adjoini…

math.NT2018

A note on the procedure to find the generic polynomial of a quotient (closely following Adelmann)

Rachel Davis

There are 3 examples in these notes. The first one is the standard example of the cubic resolvent of a quartic. The second example is exactly from Adelmann \cite{Adelmann} and give…

math.NT2016

The Galois action and cohomology of a relative homology group of Fermat Curves

Rachel Davis, Rachel Pries, Vesna Stojanoska +1

For an odd prime $p$ satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group $G_{Q (ζ_{p})}$ on the homology of the degree $p$ …

math.NT2015

Arithmetic properties of the Frobenius traces defined by a rational abelian variety (with two appendices by J-P. Serre)

Alina Carmen Cojocaru, Rachel Davis, Alice Silverberg +1

Let $A$ be an abelian variety over $Q$ of dimension $g$ such that the image of its associated absolute Galois representation $ρ_{A}$ is open in $\operatorname{GSp}_{2g}(\hat…

math.NT2014

Galois action on the homology of Fermat curves

Rachel Davis, Rachel Pries, Vesna Stojanoska +1

In his paper titled "Torsion points on Fermat Jacobians, roots of circular units and relative singular homology", Anderson determines the homology of the degree $n$ Fermat curve as…