Study of Gorenstein algebras

将代数几何中的Serre对偶理论推广到Noether代数，利用这一概念刻画了Noether代数的Gorenstein性，并给出了Gorenstein代数上的倾斜复形有Gorenstein代数作为自同态代数的充要条件.这里，一个Noether代数是交换Noether环上的模有限代数，如果它在Gorenstein基环上的对偶在导出范畴中是移位投射生成元，则称它是Gorenstein代数。

We extended Serre duality theory in algebraic geometry to Noether algebras and, using this notion, we characterized Gorensteinness of Noether algebras and provided a necessary and sufficient condition for a tilting complex over a Gorenstein algebra to have a Gorenstein algebra as an endomorphism algebra. Here, a Noether algebra is a module-finite algebra over a commutative Noether ring and is said to be a Gorenstein algebra if its dual over a Gorenstein base ring in the derived category is a shifted projective generator.