deletions | additions       diff --git a/Description/K-theorydescription.tex b/Description/K-theorydescription.tex  index 2153a39..5acf0bf 100644  --- a/Description/K-theorydescription.tex  +++ b/Description/K-theorydescription.tex 
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The key ingridienst to understand this proof are the work of Quillen around the K-theory for finite fields following the   Also it will be interesting has a discusion around the Borel's theorem on the calculation of $K_{*}(F)\times\mathbb{Q}$ $K_{*}(F)\otimes\mathbb{Q}$  for number fields. Quillen shows that for a number field $K_n(F)$ is finitely generated, the ranks of this groups has interesting arithmetic information. \end{document}