标题： 张量范畴中的交换代数 显示英文标题

标题： Commutative algebra in tensor categories

摘要： 我们发展了交换代数的一些基础，从代数几何的角度出发，在对称张量范畴中。 大多数结果建立了经典定理在某些满足特定条件的张量范畴上的张量函子的类比。 这与当前旨在通过其到不可压缩范畴的张量函子来描述张量范畴的计划是一致的。 我们特别强调了张量范畴中仿射群概形的可观子群的概念，这尤其为经典仿射群概形的可观性提供了一些进一步的见解。 显示英文摘要

摘要： We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some tensor category verifying specific conditions. This is in line with the current program which aims to describe tensor categories by their tensor functors to incompressible categories. We place particular emphasis on the notion of observable subgroups of affine group schemes in tensor categories, which in particular leads to some further insight into observability for classical affine group schemes.