The Fundamental Groupoid

  • Jakob Stix
Part of the Lecture Notes in Mathematics book series (LNM, volume 2054)


We recall the fundamental groupoid of a connected, quasi-compact scheme X as in Grothendieck (Documents Mathématiques, vol. 3, 2003) Exposé V, with special attention towards the effect of a k-structure in case of a variety Xk. Galois invariant base points are discussed and related to the profinite Kummer map. In Sect. 2.6, we address the reformulation of the section conjecture in terms of higher étale homotopy theory.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jakob Stix
    • 1
  1. 1.Mathematics Center Heidelberg (MATCH)University of HeidelbergHeidelbergGermany

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