$$\DeclareMathOperator{\mcA}{\mathcal A}$$ $$\DeclareMathOperator{\AA}{\mathbb A}$$ $$\DeclareMathOperator{\Alt}{Alt}$$ $$\DeclareMathOperator{\Arb}{Arb}$$ $$\DeclareMathOperator{\bArb}{\overline{Arb}}$$ $$\DeclareMathOperator{\Aut}{Aut}$$ $$\DeclareMathOperator{\mcC}{\mathcal C}$$ $$\DeclareMathOperator{\CC}{\mathbb C}$$ $$\DeclareMathOperator{\cchar}{char}$$ $$\DeclareMathOperator{\co}{co}$$ $$\DeclareMathOperator{\Col}{Col}$$ $$\DeclareMathOperator{\Gal}{Gal}$$ $$\DeclareMathOperator{\GG}{\mathbb G}$$ $$\DeclareMathOperator{\mcH}{\mathcal H}$$ $$\DeclareMathOperator{\haus}{haus}$$ $$\DeclareMathOperator{\mcI}{\mathcal I}$$ $$\DeclareMathOperator{\id}{id}$$ $$\DeclareMathOperator{\Id}{Id}$$ $$\DeclareMathOperator{\img}{img}$$ $$\DeclareMathOperator{\IMG}{IMG}$$ $$\DeclareMathOperator{\bIMG}{\overline{IMG}}$$ $$\DeclareMathOperator{\barK}{\overline{K}}$$ $$\DeclareMathOperator{\Mon}{Mon}$$ $$\DeclareMathOperator{\bMon}{\overline{Mon}}$$ $$\DeclareMathOperator{\mcM}{\mathcal M}$$ $$\DeclareMathOperator{\mcO}{\mathcal O}$$ $$\DeclareMathOperator{\mcP}{\mathcal P}$$ $$\DeclareMathOperator{\ncl}{ncl}$$ $$\DeclareMathOperator{\NN}{\mathbb N}$$ $$\DeclareMathOperator{\NP}{NP}$$ $$\DeclareMathOperator{\ord}{ord}$$ $$\DeclareMathOperator{\PP}{\mathbb P}$$ $$\DeclareMathOperator{\PGL}{PGL}$$ $$\DeclareMathOperator{\piet}{\pi_1^{\acute{e}t}}$$ $$\DeclareMathOperator{\QQ}{\mathbb Q}$$ $$\DeclareMathOperator{\mcQ}{\mathcal Q}$$ $$\DeclareMathOperator{\rad}{rad}$$ $$\DeclareMathOperator{\mcS}{\mathcal S}$$ $$\DeclareMathOperator{\sgn}{sgn}$$ $$\DeclareMathOperator{\Spec}{Spec}$$ $$\DeclareMathOperator{\Stab}{Stab}$$ $$\DeclareMathOperator{\Sym}{Sym}$$ $$\DeclareMathOperator{\mcW}{\mathcal W}$$ $$\DeclareMathOperator{\ZZ}{\mathbb Z}$$ $$\newcommand{\ab}{\textrm{ab}}$$ $$\newcommand{\cyc}{\textrm{cyc}}$$ $$\renewcommand{\epsilon}{\varepsilon}$$ $$\newcommand{\inv}{^{-1}}$$ $$\newcommand{\llangle}{\langle\hspace{-0.5em}\langle}$$ $$\newcommand{\normal}{\triangleleft}$$ $$\newcommand{\odometer}{\omega}$$ $$\newcommand{\Odometer}{\Omega}$$ $$\newcommand{\OK}{\mcO_K}$$ $$\newcommand{\pp}{\mathfrak p}$$ $$\newcommand\res{\!\!\mid\!\!}$$ $$\newcommand{\rrangle}{\rangle\hspace{-0.5em}\rangle}$$ $$\newcommand{\sep}{^{sep}}$$ $$\newcommand{\wh}{\widehat}$$

Research

Author

Ophelia Adams

Published

November 13, 2025

A small brown rabbit with a white nose reading a book (Introduction to Commutative Algebra by Atiyah and Macdonald).

About

I am in the process of gathering my research onto this site. It is my hope that the HTML verions will be more accessible than PDFs (see arXiv’s discussion). This format also affords conveniences not available to PDFs, like a functional search bar and hoverable tooltips for references to corollaries/lemmas/propositions/theorems.

Links to the journal or arXiv version are included where applicable. These versions should generally be a close match modulo typos or notational tweaks; larger deviations, if any, will be pointed out. For convenience, all references are condensed into a single bibliography.

The numbering on this site is continuous across articles and is subject to regular change when pages are added. The initial move was accomplished by a series of increasingly contorted regular expressions, so there may be some typographic oddities.