1
vote
1answer
247 views

Cohomology after completion

I've been scouring google and asking friend about something I was certain must be absolutely the easiest thing to people who do homological algebra, and none seem to know the answer to this, so if ...
2
votes
3answers
368 views

Computing the cardinality of cohomology groups

I hope this question is not unreasonably broad. It is about calculating or at least bounding the cardinality of cohomology groups in case they are finite. Let us assume we are given a group $G$ and a ...
8
votes
1answer
418 views

Which information can be obtained from Poincaré series ?

If $A= \bigoplus_{i\ge 0}A_i$ is a graded commutative Noetherian algebra over a field, its Poincaré series is given by $P(t) = \sum_{i\ge 0} \dim(A_i)t^i$. Although the definition of $P(t)$ only ...
2
votes
2answers
315 views

Whether such an algebra has to be the Group algebra

Let $\mathbb C$ be the field of the complex numbers, $\mathbb Q$ the field of the rational numbers. Let $G$ be an additive subgroup of $\mathbb Q$. $R$ is an commutative algebra over $\mathbb C$, ...
3
votes
2answers
662 views

Invariants and base change

Suppose $R$ is a Noetherian commutative ring, and $M$ a finite free $R$-module, with an action of a finitely generated discrete group $G$ by $R$-linear maps. Is there any homological condition on ...