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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Notes
- 1.
The apparently natural notation \(\mathfrak{X}_{\text{red}}\) is classically used to denote the scheme defined by the largest ideal of definition of \(\mathfrak{X}\).
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Chambert-Loir, A., Nicaise, J., Sebag, J. (2018). Greenberg Schemes. In: Motivic Integration. Progress in Mathematics, vol 325. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-7887-8_4
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DOI: https://doi.org/10.1007/978-1-4939-7887-8_4
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