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\title{Quillen's local parameter conjecture\\[3pt]
       in dimension four}
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\date{}
\begin{document}
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\begin{abstract}
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\noindent\textbf{Keywords.} Projective modules; local Quillen problem;
mixed characteristic; algebraic $K$-theory; hermitian $K$-theory;
Milnor--Witt theory.

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\part{The completion criterion}
\input{sections/00_theorem_and_bridge}
\par\bigskip\needspace{12\baselineskip}
\part{Integral degree-two algebraic K-theory}
\input{sections/01_k2}
\par\bigskip\needspace{12\baselineskip}
\part{Hermitian theory and local motivic cohomology}
\input{sections/02_hermitian_and_support}
\input{sections/03_motivic_local_comparisons}
\par\bigskip\needspace{12\baselineskip}
\part{Global vanishing and projective modules}
\input{sections/04_global_mw4}
\input{sections/05_projective_conclusion}
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\input{frontmatter/ai_disclosure}
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\addcontentsline{toc}{section}{References}
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\bibliography{references,references_hermitian,references_motivic,references_bridge,references_k2,references_context}
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