\relax \providecommand\hyper@newdestlabel[2]{} \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 8/27/2024}}{5}{section*.1}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{1}{The ring of integers \(\mathcal {O} _K\) }}{6}{chapter.1}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 8/29/2024}}{7}{section*.2}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Preliminaries from the theory of fields}}{8}{section*.3}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 9/3/2024}}{9}{section*.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{The Discriminant}}{9}{section*.5}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 9/5/2024}}{11}{section*.6}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{2}{Ideals}}{13}{chapter.2}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 9/10/2024}}{15}{section*.7}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Decomposition of primes in \(\mathcal {O}_K\)}}{16}{section*.8}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 9/12/2024}}{17}{section*.9}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 9/17/2024}}{19}{section*.10}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{The Quadratic Reciprocity Law (QRL):}}{20}{section*.11}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{3}{Lattices}}{22}{chapter.3}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 9/19/2024}}{22}{section*.12}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{4}{Geometry of Numbers}}{25}{chapter.4}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 9/24/2024}}{25}{section*.13}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{5}{The Class Number}}{29}{chapter.5}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 9/26/2024}}{29}{section*.14}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{6}{Dirichlet's Theorem on Units}}{31}{chapter.6}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 10/1/2024}}{31}{section*.15}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 10/3/2024}}{33}{section*.16}\protected@file@percent } \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Fundamental Units of Quadratic Fields}}{34}{table.6.1}\protected@file@percent } \newlabel{tab:funit}{{1}{34}{Fundamental Units of Quadratic Fields}{table.6.1}{}} \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{7}{Extensions of Dedekind Domains}}{36}{chapter.7}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 10/8/2024}}{37}{section*.17}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{8}{Ramification Theory}}{40}{chapter.8}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 10/10/2024}}{40}{section*.18}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 10/15/2024}}{43}{section*.19}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{9}{Absolute Values on Fields}}{44}{chapter.9}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Topology}}{44}{section*.20}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 10/17/2024}}{45}{section*.21}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Completions}}{47}{section*.22}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 10/22/2024}}{48}{section*.23}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Extension of Absolute Values}}{49}{section*.24}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 10/24/2024}}{50}{section*.25}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 10/29/2024}}{52}{section*.26}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 10/31/2024}}{54}{section*.27}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{10}{Residue Class Degree and Ramification Index}}{57}{chapter.10}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 11/5/2024}}{57}{section*.28}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 11/7/2024}}{59}{section*.29}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 11/12/2024}}{60}{section*.30}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 11/14/2024}}{62}{section*.31}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{11}{Local Fields}}{64}{chapter.11}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 11/19/2024}}{66}{section*.32}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 11/21/2024}}{67}{section*.33}\protected@file@percent } \@writefile{toc}{\contentsline {chapter}{\tocchapter {Chapter}{12}{Lubin-Tate Theory}}{69}{chapter.12}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Formal Groups}}{69}{section*.34}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 12/3/2024}}{70}{section*.35}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 12/5/2024}}{71}{section*.36}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Tuesday, 12/10/2024}}{73}{section*.37}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Local Complex Multiplication}}{73}{section*.38}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{}{Thursday, 12/12/2024}}{75}{section*.39}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Lubin-Tate theory and the maximal abelian extension}}{75}{section*.40}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Ramification Groups}}{76}{section*.41}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{}{Upper ramification numbering}}{76}{section*.42}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Herbrand Function}}{77}{figure.12.1}\protected@file@percent } \newlabel{tocindent-1}{0pt} \newlabel{tocindent0}{61.69456pt} \newlabel{tocindent1}{0pt} \newlabel{tocindent2}{0pt} \newlabel{tocindent3}{0pt} \gdef \@abspage@last{78}