In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Zariski–Riemann spaces were introduced by Zariski (1940, 1944) who (rather confusingly) called them Riemann manifolds or Riemann surfaces.
In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Zariski–Riemann spaces were introduced by Zariski (1940, 1944) who (rather confusingly) called them Riemann manifolds or Riemann surfaces.
Source: Wikipedia "Zariski–Riemann space" · CC BY-SA 4.0
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