论文标题
Grothendieck Monoid的范围：对SERRE子类别进行分类和重建定理
The spectrum of Grothendieck monoid: classifying Serre subcategories and reconstruction theorem
论文作者
论文摘要
精确类别的Grothendieck Monoid是Grothendieck集团的单体版本。我们使用它来对确切类别的Serre子类别进行分类，并重建Noetherian方案的拓扑。我们首先在（i）（i）确切类别的Serre子类别，（ii）其Grothendieck Monoid的面孔和（iii）其Grothendieck Monoid的单体频谱之间构造了射击。通过使用（ii），我们对与有限维代数相关的确切类别的Serre子类别进行分类。特别是，我们确定了光滑的投射曲线上相干滑轮类别的肉眼。通过使用（iii），我们对Serre子类别集进行了拓扑。结果，我们从Grothendieck Monoid中恢复了Noetherian计划的拓扑。
The Grothendieck monoid of an exact category is a monoid version of the Grothendieck group. We use it to classify Serre subcategories of an exact category and to reconstruct the topology of a noetherian scheme. We first construct bijections between (i) the set of Serre subcategories of an exact category, (ii) the set of faces of its Grothendieck monoid, and (iii) the monoid spectrum of its Grothendieck monoid. By using (ii), we classify Serre subcategories of exact categories related to a finite dimensional algebra and a smooth projective curve. In particular, we determine the Grothendieck monoid of the category of coherent sheaves on a smooth projective curve. By using (iii), we introduce a topology on the set of Serre subcategories. As a consequence, we recover the topology of a noetherian scheme from the Grothendieck monoid.
