|Budget Amount *help
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
In 1996 we introduced a new theory of pro-affine algebras and ind-affine varieties over an algebraically closed ground field K. This theory has now been thoroughly reviewed and rebuilt in accordance with Grothendieckian theory of algebraic schemes, albeit ours being still over a field K. We have developped, amoung other things, ideal theory and localization theory for pro-affine algebras, and have constructed the dual objects of this type of algebras, which are naturally called ind-affine schemes. A sheaf of pro-affine algebras are built over each ind-affine schemes, and its stalk appropriately defined will be a pro-affine local ring. These results have been written up in a paper, "Some Basic Theorems on Pro-Affine Algebras and Ind-Affine Schemes," and this paper will be submitted for pubication in the near future. As a by-product we have obtained a new proof of the fact that the automorphism group of an affine space is ind-affine, and we also proved that he set of morphisms of affine varieties is ind-affine. These results have been written into a paper, "Morphisms of affine varieties as ind-affine schemes," and this one will be published after the final editing.
この研究の間に,いわば副産物として(1)アフィン空間の自己同型群がind-affineであることの新証明,と(2)アフィン多様体間の射の全体からなる集合に自然にind-affine構造が入れられるということの証明,とができた。この結果をまとめて論文"Sets of Morphisms as ind-affine Schemes"は若干の編集作業を除いては完成しており,近日中に投稿されるであろう。