thesis.sty

% !TEX root = Daniel-Miller-thesis.tex


% Operators.
\DeclareMathOperator{\Ad}{Ad}    % Adjoint representation.
\DeclareMathOperator{\cdf}{cdf}  % Cumulative distribution function.
\DeclareMathOperator{\D}{D}      % Discrepancy.
\DeclareMathOperator{\End}{End}  % Ring of endomorphisms.
\DeclareMathOperator{\Gal}{Gal}  % Galois group.
\DeclareMathOperator{\GL}{GL}    % General Linear Group.
\DeclareMathOperator{\h}{H}      % (Group) cohomology.
\DeclareMathOperator{\im}{im}    % Image of a map. 
\DeclareMathOperator{\Li}{Li}    % (Eulerian) logarithmic integral.
\DeclareMathOperator{\Lie}{Lie}  % Lie algebra
\DeclareMathOperator{\N}{N}      % Norm map.
\DeclareMathOperator{\ord}{ord}  % Order of a zero.
\DeclareMathOperator{\R}{R}      % restriction of scalars
\DeclareMathOperator{\rk}{rk}    % Rank of a group.
\DeclareMathOperator{\sgn}{sgn}  % Sign of a real number.
\DeclareMathOperator{\SO}{SO}    % Special orthogonal group.
\DeclareMathOperator{\SU}{SU}    % Special unitary group.
\DeclareMathOperator{\sym}{sym}  % Symmetric power.
\DeclareMathOperator{\tr}{tr}    % Trace.
\DeclareMathOperator{\X}{X}      % Group of characters of a torus.
\DeclareMathOperator{\Var}{Var}  % Variation of a function.


% Bold letters.
\newcommand{\ba}{{\boldsymbol a}}
\newcommand{\bA}{\mathbf{A}}
\newcommand{\balpha}{{\boldsymbol\alpha}}
\newcommand{\bmu}{{\boldsymbol\mu}}
\newcommand{\bepsilon}{{\boldsymbol\epsilon}}
\newcommand{\bC}{\mathbf{C}}
\newcommand{\bF}{\mathbf{F}}
\newcommand{\bN}{\mathbf{N}}
\newcommand{\bQ}{\mathbf{Q}}
\newcommand{\bR}{\mathbf{R}}
\newcommand{\brho}{{\boldsymbol\rho}}
\newcommand{\bT}{\mathbf{T}}
\newcommand{\btheta}{{\boldsymbol\theta}}
\newcommand{\bv}{{\boldsymbol v}}
\newcommand{\bx}{{\boldsymbol x}}
\newcommand{\bvx}{\vec{\boldsymbol x}}
\newcommand{\by}{{\boldsymbol y}}
\newcommand{\bz}{{\boldsymbol z}}
\newcommand{\bZ}{\mathbf{Z}}
\newcommand{\dQ}{\mathbf{Q}}


% Fraktur letters.
\newcommand{\fa}{\mathfrak{a}}
\newcommand{\fp}{\mathfrak{p}}
\newcommand{\ft}{\mathfrak{t}}


% Vectors.
\newcommand{\va}{\vec{a}}
\newcommand{\vb}{\vec{b}}
\newcommand{\vinfty}{\vec{\infty}}
\newcommand{\vm}{\vec{m}}
\newcommand{\vs}{\vec{s}}
\newcommand{\vt}{\vec{t}}
\newcommand{\vx}{\vec{x}}
\newcommand{\vy}{\vec{y}}
\newcommand{\vz}{\vec{z}}
\newcommand{\vzero}{\vec{0}}


% Miscellaneous symbols.
\newcommand{\dd}{\mathrm{d}}                 % Differential.
\newcommand{\frob}{\mathrm{fr}}              % Frobenius. 
\newcommand{\Gm}{\mathbf{G}_\mathrm{m}}      % Multiplicative group.
\newcommand{\nr}{\mathrm{nr}}                % Non-ramified cohomology.
\newcommand{\pow}[1]{\llbracket#1\rrbracket} % Ring of power series.
\newcommand{\ram}{\mathrm{ram}}              % Set of ramified primes.
\newcommand{\ST}{\mathrm{ST}}                % Sato--Tate group.
\newcommand{\tate}{\mathrm{T}}               % Tate module


% Matrices.
\newcommand{\smat}[4]{
	\left(\begin{smallmatrix} 
		#1 & #2 \\ 
		#3 & #4 
	\end{smallmatrix}\right)
}
\newcommand{\svec}[2]{
	\left(\begin{smallmatrix} 
		#1 \\ 
		#2 
	\end{smallmatrix} \right)
}



% Tate--Shafarevich groups.
\DeclareFontFamily{U}{wncy}{}
\DeclareFontShape{U}{wncy}{m}{n}{<->wncyr10}{}
\DeclareSymbolFont{mcy}{U}{wncy}{m}{n}
\DeclareMathSymbol{\Sha}{\mathord}{mcy}{"58}


% Environments. 
\newtheorem{conjecture}[subsection]{Conjecture}
\newtheorem{corollary}[subsection]{Corollary}
\newtheorem{lemma}[subsection]{Lemma}
\newtheorem{theorem}[subsection]{Theorem}
\theoremstyle{definition}
\newtheorem{definition}[subsection]{Definition}