# Tagged Questions

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**1**answer

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**

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**3**answers

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

**1**answer

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 PoincarĂ© series is given by $P(t) = \sum_{i\ge 0} \dim(A_i)t^i$. Although the definition of $P(t)$ only ...

**2**

votes

**2**answers

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

**2**answers

663 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 ...