Admissible complexes Clause Samples
Admissible complexes. In this section, we will define the category of ‘admissible complexes’ which will be studied in detail in this thesis. We will give examples of objects in this category that arise naturally from the arithmetic context in the next section. At the outset, we fix a Dedekind domain R of characteristic 0 with field of fractions F and a commutative R-order A that spans a separable F -algebra A := F ⊗R A.
2.3.1 The key definitions
2.3.1. The category Da(A) of ‘admissible perfect complexes of A-modules’ is defined to be the full subcategory of D(A) comprising complexes C = (Ci)i∈Z that satisfy the following four conditions:
Admissible complexes. In this subsection we describe the relevance of the maps Π𝐶•,𝑓 and Θ𝐶•,𝑓 to the arithmetic setting. To do this we first make the following definition: