symmetric monoidal (∞,1)-category of spectra
An entire functional calculus algebra is a product-preserving functor
where is the category of finite-dimensional complex vector spaces and holomorphic maps.
This is in complete analogy to C^∞-rings, and EFC-algebras are applicable in similar contexts.
The category of globally finitely presented Stein spaces is contravariantly equivalent to the category of finitely presented EFC-algebras. The equivalence functor sends a Stein space to its EFC-algebra of global sections.
The category of Stein spaces of finite embedding dimension is contravariantly equivalent to the category of finitely generated EFC-algebras. The equivalence functor sends a Stein space to its EFC-algebra of global sections.
These statements can thus be rightfully known as Stein duality.
Alexei Pirkovskii, Holomorphically finitely generated algebras, Journal of Noncommutative Geometry 9 (2015), 215–264 (arXiv:1304.1991, doi:10.4171/JNCG/192).
J. P. Pridham, A differential graded model for derived analytic geometry, Advances in Mathematics 360 (2020), 106922. arXiv:1805.08538v1, doi:10.1016/j.aim.2019.106922.
Last revised on October 18, 2021 at 15:51:50. See the history of this page for a list of all contributions to it.