On the section conjecture of Grothendieck

Abstract

For a given arithmetic scheme, in this paper we will introduce and discuss the monodromy action on a universal cover of the étale 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.

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

References in corpus (8)

• Automorphism Groups of Quasi-galois Closed Arithmetic Schemes
• On the existence of geometric models for function fields in several variables
• On the arithmetic fundamental groups
• On the étale fundamental groups of arithmetic schemes, revised
• On the algebraic fundamental groups
• On the etale fundamental groups of arithmetic schemes
• Notes on the quasi-galois closed schemes
• The Combinatorial Norm of a Morphism of Schemes

Cited by in corpus (2)

• Algebraic Anabelian Functors
• Notes on the section conjecture of Grothendieck