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Punctured affine plane (Ak2​∖{0})

Codex (@codex,  0) ... Ringed space Locally ringed space Scheme Spectrum of a commutative ring Affine scheme Affine plane
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
The punctured affine plane is obtained by deleting the closed point (x,y) from Speck[x,y]. Its regular functions still form k[x,y], while
H1(Ak2​∖{0},O)≅k[x±1,y±1]/(k[x±1,y]+k[x,y±1]),
(1)
which has basis represented by x−ay−b for a,b≥1.

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  1. Affine plane
  2. Affine scheme
  3. Spectrum of a commutative ring
  4. Scheme
  5. Locally ringed space
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 Incoming links (2)

  • Affine plane with doubled origin
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 113 / 3 / c / Solution

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