完全无环逼近
Totally acyclic approximations
摘要：
设$R$是交换局部环.研究了由全无圈$R$-复形构成的$R$-复形同伦范畴的子范畴.特别地，在$Q\to R$是满射局部环同态使得$R$在$Q$上具有有限投射维数的情形下，我们在全无环$R$ -复形的同伦范畴和$Q$ -复形的同伦范畴之间定义了一个伴随函子对，它类似于$R$和$Q$模范畴之间的经典伴随函子对.我们从单位和计数的角度给出了这一附加的详细证明。因此，我们得到了全无环$R$ -复形由全无环$Q$ -复形逼近的精确概念。
英文摘要：
Let $R$ be a commutative local ring. We study the subcategory of the homotopy category of $R$-complexes consisting of the totally acyclic $R$-complexes. In particular, in the context where $Q\to R$ is a surjective local ring homomorphism such that $R$ has finite projective dimension over $Q$, we define an adjoint pair of functors between the homotopy category of totally acyclic $R$-complexes and that of $Q$-complexes, which are analogous to the classical adjoint pair between the module categories of $R$ and $Q$. We give detailed proofs of the adjunction in terms of the unit and counit. As a consequence, one obtains a precise notion of approximations of totally acyclic $R$-complexes by totally acyclic $Q$-complexes.
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