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Results tagged with ac.commutative-algebra
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user 17907
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
3
votes
Generalization of Weak Nullstellensatz?
Or see Proposition 2.4.6 in Bjorn Poonen's book Rational Points on Varieties (link). This is almost exactly the result you conjectured, just a bit more general:
Let $X$ be a $k$-variety. Then the map …
- 4,745
7
votes
Set of primes $p$ such that $\mathrm{Hom}(A, \mathbb{F}_p)=\emptyset$
Here's a sketch of an answer. I think the answer is that you can get three types of sets: (i) finite sets, (ii) co-finite sets, and (iii) sets of the form
$$
S_f = \{ p : f(x) ~ \textrm{has a root in …
- 4,745
4
votes
On the fixed point of automorphism of $\mathbb F_3[[T]]$
Let's write $R$ for $\mathbb{F}_3[[T]]$ and $K$ for its fraction field. Suppose $t \in R \setminus \mathbb{F}_3$ satisfies $\sigma(t)=t$. I claim that $\sigma$ then has finite order.
Suppose first tha …
- 4,745
4
votes
Pythagorean number in Artin's theorem on nonnegative rational fractions
Apparently, we have $N \leq 2^n$. See these slides by Jean-Louis Colliot-Thélène, belonging to a lecture he gave in Leiden in 2011:
http://www.math.u-psud.fr/~colliot/Kloostermanlezing.pdf
First, he w …
- 4,745
1
vote
How to show an invariant subfield of rational function field $\mathbb{Q}(x)$ under a certain...
The answer as to the surjectivity of $\alpha$ is no. As in algebraic number theory, the simplest way to prove that an element is not a norm is by local considerations. Let us consider
$$
y=\frac{(x^3- …