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Greenberg Schemes

  • Antoine Chambert-Loir
  • Johannes Nicaise
  • Julien Sebag
Chapter
Part of the Progress in Mathematics book series (PM, volume 325)

Abstract

Let R be a complete discrete valuation ring, let \(\mathfrak{m}\) be its maximal ideal, and let k be its residue field. When R = k[​[t]​] and X is a k-scheme, we defined in chapter  3 the schemes of jets \(\mathcal{L}_{n}(X/k)\) and the scheme of arcs \(\mathcal{L}_{\infty }(X/k)\) on X whose k-points are in canonical bijection with \(X(R/\mathfrak{m}^{n+1})\) and X(R), respectively.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Antoine Chambert-Loir
    • 1
  • Johannes Nicaise
    • 2
  • Julien Sebag
    • 3
  1. 1.Département de MathématiquesUniversité Paris-Sud OrsayOrsayFrance
  2. 2.Department of MathematicsUniversity of LeuvenHeverleeBelgium
  3. 3.Département de MathématiquesUniversité de Rennes 1RennesFrance

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