English

On the section conjecture of Grothendieck

Algebraic Geometry 2009-12-21 v4 Number Theory

Abstract

For a given arithmetic scheme, in this paper we will introduce and discuss the monodromy action on a universal cover of the \'etale fundamental group and the monodromy action on an \emph{sp}-completion constructed by the graph functor, respectively; then by these results we will give a proof of the section conjecture of Grothendieck for arithmetic schemes.

Keywords

Cite

@article{arxiv.0911.1523,
  title  = {On the section conjecture of Grothendieck},
  author = {Feng-Wen An},
  journal= {arXiv preprint arXiv:0911.1523},
  year   = {2009}
}

Comments

22 pages. Made Changes in Page 4, Def 2.3; Page 5, "essential equal". Deleted Page 6, footnote. Removed Typos: "integral scheme" changed into "integral variety (-ies)" in Remark 5.8, Theorem 5.9, Lemma 5.10, and Page 15, section 6