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Okay, so I'm pretty sure I have a sort-of answer for this for $f=x+y+\sum_{i,j>0}a_{ij}x^iy^j$, though it's not a closed form at all. With a bit of fiddling one can see that $$ f\circ f = \sum_{i,j> …

This is essentially a request for counterexamples, since I know so few $n$-buds (or as some might say, formal group law $n$-chunks). One notices that the only $1$-bud of maximal degree 1 is the addit …

There seems to be quite a bit of theory developed to deal with "stable homotopy" in the sense of the derived category of a Noetherian ring, or just any situation where the endomorphism ring of the gen …

Perhaps this question is too elementary, but if it's written down anywhere, I'd love to know about it. Suppose I have a power series $f\in R[[x,y]]$ for some commutative, unital ring. I've recently be …

It's known that a pure morphism of commutative rings $\phi:A\to B$ is of effective descent for the stack of modules. In other words if $\phi$ is pure one can recover $Mod(A)$ as the 2-limit of a trunc …

For a homomorphism of commutative rings $f:R\to S$, there are at least two notions of a descent datum for this map. One of these is to be an $S$-module $M$, with an isomorphism $M\otimes_R S\cong S\ot …