论文标题
Fréchet模块和下降
Fréchet Modules and Descent
论文作者
论文摘要
我们研究了Banach环上IND-Banach模块的研究的几个方面，从而综合了同源代数的某些方面和功能分析。这包括一项研究核模块和相对于投射张量产品平坦的模块的研究。我们还研究了Metrizable和FréchetInd-Banach模块。我们将Banach环的投影限制作为索引。我们研究了有关内核和可数产品的射击产品的精确性。作为应用，我们描述了Banach代数几何形状中的准加固模块的理论。我们证明了在各种分析和算术环境中的准连续模块的下降定理。
We study several aspects of the study of Ind-Banach modules over Banach rings thereby synthesizing some aspects of homological algebra and functional analysis. This includes a study of nuclear modules and of modules which are flat with respect to the projective tensor product. We also study metrizable and Fréchet Ind-Banach modules. We give explicit descriptions of projective limits of Banach rings as ind-objects. We study exactness properties of projective tensor product with respect to kernels and countable products. As applications, we describe a theory of quasi-coherent modules in Banach algebraic geometry. We prove descent theorems for quasi-coherent modules in various analytic and arithmetic contexts.
