Hochster duality

Given a coherent space, $X$, a new topology may be constructed by taking as basic open subsets the closed sets of $X$ with quasicompact complements. This space $X^{\vee}$ is called the *Hochster dual* of $X$. The space $X^{\vee}$ is also coherent and $X^{\vee \vee} = X$.

The Hochster dual of a distributive lattice is the opposite lattice. The Hochster dual of a coherent frame is its join completion.

The original source is

- M. Hochster,
*Prime ideal structure in commutative rings*, Transactions of the American Mathematical Society, 142, (1969), 43–60

See also:

- Joachim Kock, Wolfgang Pitsch,
*Hochster duality in derived categories and point-free reconstruction of schemes*, (arXiv: 1305.1503)

Last revised on May 19, 2020 at 13:27:11. See the history of this page for a list of all contributions to it.