nLab structure sheaf

Idea

For a ringed topos $(\mathcal{X}, \mathcal{O})$ the ring object $\mathcal{O} \in \mathcal{X}$ is called the structure sheaf.

More generally, for $\mathcal{G}$ a geometry (for structured (∞,1)-toposes), a structured (∞,1)-topos

$$\mathcal{O} : \mathcal{G} \to \mathcal{X}$$

is an (∞,1)-topos equipped with a $\mathcal{G}$-valued structure sheaf presented by the finite-limits-preserving and cover-preserving (∞,1)-functor $\mathcal{O}$.

Related concepts

• sheaf of meromorphic functions

• sheaf of rational functions

References

• James Milne, section 6 of Lectures on Étale Cohomology

category: sheaf theory, algebraic geometry