An open subscheme of a scheme 
is a subscheme 
whose inclusion 
is an open immersion.
Its underlying space is an open set of 
, and its structure sheaf
is the restriction of 
to that open set, namely the restriction of a
sheaf.
Open Subscheme
See also
Closed Subscheme, Open Immersion, Open Set, Structure Sheaf, SubschemeExplore with Wolfram|Alpha
References
Grothendieck, A. and Dieudonné, J. "Éléments de géométrie algébrique. I. Le langage des schémas." Publ. Math. IHES 4, 5-228, 1960. https://doi.org/10.1007/BF02684778.The Stacks Project Authors. "Immersions of Schemes." §26.10 in The Stacks Project, Tag 01IM, 2026. https://stacks.math.columbia.edu/tag/01IM.Cite this as:
Weisstein, Eric W. "Open Subscheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OpenSubscheme.html