论文标题
Grothendieck组，凸锥和最大Cohen-Macaulay点
Grothendieck groups, convex cones and maximal Cohen-Macaulay points
论文作者
论文摘要
让A成为一个可交换的Noetherian戒指。令H（a）为伪零模块生成的子组有限生成的A模块的Grothendieck组的商。假设实际矢量空间h（a）_r = h（a）\ otimes_z r具有有限的维度。令C（A）（分别C_R（A））为H（A）_R中的凸锥，由最大Cohen-Macaulay a-modules跨度（resp。maximalcohen-macaulay a rank r）。我们探索C（a）的内部，闭合和边界以及凸多角形子官。我们为A提供了各种等效条件，即在C_R（a）的C_R（a）中，只有有限的等级r最大cohen-macaulay点（a）。最后，我们将排名第一的最大Cohen-Macaulay模块视为Divisor类组Cl（a）的元素。
Let A be a commutative noetherian ring. Let H(A) be the quotient of the Grothendieck group of finitely generated A-modules by the subgroup generated by pseudo-zero modules. Suppose that the real vector space H(A)_R = H(A) \otimes_Z R has finite dimension. Let C(A) (resp. C_r(A)) be the convex cone in H(A)_R spanned by maximal Cohen-Macaulay A-modules (resp. maximal Cohen-Macaulay A-modules of rank r). We explore the interior, closure and boundary, and convex polyhedral subcones of C(A). We provide various equivalent conditions for A to have only finitely many rank r maximal Cohen-Macaulay points in C_r(A) in terms of topological properties of C_r(A). Finally, we consider maximal Cohen-Macaulay modules of rank one as elements of the divisor class group Cl(A).
