粉丝

摘要：

（抽象的）扇范畴对于幺半群范畴的意义就像概型范畴对于环范畴的意义一样：扇是通过沿着开嵌入粘合幺半群的谱而得到的。在这里，我们研究基本的代数几何的球迷：相干层，群球迷，仿射映射，平面映射，适当的地图，等等。本研究的动机是这样一个事实，即球迷的范畴是在所有其他合理的几何范畴（计划，可微空间，解析空间等），以及所有这些类别的“日志”版本。

英文摘要：

The category of (abstract) fans is to the category of monoids what the category of schemes is to the category of rings: a fan is obtained by gluing spectra of monoids along open embeddings. Here we study the basic algebraic geometry of fans: coherent sheaves, group fans, affine maps, flat maps, proper maps, and so forth. This study is motivated by the fact that the category of fans lies over all other reasonably geometric categories (schemes, differentiable spaces, analytic spaces, etc) as well as the "log" versions of all such categories.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。