deletions | additions       diff --git a/sectionPlan_of_the_T.tex b/sectionPlan_of_the_T.tex  index d8462c1..dfa082e 100644  --- a/sectionPlan_of_the_T.tex  +++ b/sectionPlan_of_the_T.tex 
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\subsection{Introduction to K-theory}  \paragraph{Talk 1: Definition of $K_0$, $K_1$ and of higher $K_i$ via Quillen's plus construction.} ``Classical'' K-theory}  In this talk we will review $K_0$, $K_1$ and $K_2$ of rings.  Follow Srinivas, chapter 1.  \begin{itemize}  \item Remark it is an $H$ -space so we can compute the rational homotopy groups mention Cartan-Serre's theorem.  \item Remark $K$-theory with finite coeficients.  \end{itemize}  \paragraph{Talk 2: Quillen plus construction}  \subsection{Norm-Residue Homomorphism (Merkurjev-Suslin theorem)}  \paragraph{Talk 2: 3:  Construction of the norm-residue homomorphism}\paragraph{Talk 3: }  \paragraph{Talk 4: }  \paragraph{Talk 5: }  \subsection{Borel's theorem}  \paragraph{Talk 5: 6:  Rank of $K_n$ over number fields} \begin{itemize}  \item Show how to reduce the problem to the computation of the real cohomology of $SL(F)$. Borel determined the ring $H^*(SL_m(R);\mathbb{Q})$ and its dual coalgebra. Relate the primitive elementes of to the idecomposables elementes and finally to $H^*(SL(O_F),\mathbb{R})$. 
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The pourpuse of this talk is assuming the computation of the real cohomology of $SL(F)$ prove Theorem \ref{Borel-Ranks}.  \end{itemize}  \paragraph{Talk 6: 7:  The Borel regulator.} (Burgos Gil Book)  \paragraph{Talk 7:} 8:}  \subsection{Rigidity theorem}  \paragraph{Talk 8: 9:  K-theory for finite fields} Quillen's work in Adam's conjecture  \paragraph{Talk 9: 10:  K-theory of algebraically closed fields} The purpuse of this section is prove one of the Quillen-Lichtembaum conjectures  \begin{theo} 
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Corollary 1.3.1 and Proposition 1.4   The main references for this part are: Weibel's book \cite{Kbook} VI.1 and Suslin's paper  \paragraph{Talk 10: 11:  $K_3$ of fields and the relation with the Bloch group} \bibliographystyle{alpha}