Exercises and discussion topics

This ring structure is complicated. In particular it is not the product structure. However, this way of defining the Witt vectors gives us a useful approach for how to prove things about them. Roughly speaking, to prove something about W(A) one can use the ghost map to transfer the problem to the ring A with its product structure. This works especially well if A is p-torsion free since then considering the definition of w the ghost map is injective. One can then hope to cover the general case by finding a surjection B → A from a p-torsion free algebra B.