Change of Order
Here we shall give a unified treatment both for “going up” and for “going down”. Even where no involution is involved, our approach throws new light on the problem, and it is in this context that the superiority of the Hom group language is most marked. Although many results, and in particular parts of Theorems 8 and 10 are more general, we shall make again the blanket assumptions that O is global or local or a field — as in the preceding chapters. This is preferable to having at each stage lengthy detailed statements of the precise conditions under which some assertion holds. The “generality” game is left to the reader, be he so inclined.
KeywordsCommutative Diagram Galois Group Left Action Left Hand Column Hand Column
Unable to display preview. Download preview PDF.