ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 13 Kambayashi, Tatsuji, Tokyo Denki University, Japan A Nullstellensatz for Pro-Affine Algebras With a view toward application to the Jacobian Problem, a theory of proaffine algebras and ind-affine varieties has been presented in my paper, J. Alg. 185(1996), 481–501. Let A = lim_{←} A_{i} be a pro-affine K-algebra with K algebraically closed, and assume all A_{i} to be of finite type over K. Define the radical ℜ(A) and the nilradical 𝔑(A) of A, resp. , to be the intersections of all open maximal ideals and of all open prime ideals of A, resp. We can then prove

Theorem. ℜ(A) = 𝔑(A).

A more complete theory of pro-affine algebras and ind-affine schemes, including the above and a localization theory, will be published elsewhere.