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

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Showing 2018Show all

4 papers · 1 filter

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…