| Abstract: The aim of this note is to prove certain compatibilities of determinant functors with spectral sequences and (co)homology thereby extending results of Breuning and Burns [2] and refining a description by Knudsen in [9]. It turns out that the determinant behaves as well as one would have expected in this regard, only that we were not able to find references for it in the literature. The results are crucial for descent calculations in the context of Iwasawa theory [12] or Equivariant Tamagawa Number Conjectures [4, 5, 6]. |