## All Questions

2answers
499 views

### Is K(R-Mod) compactly generated when R is an artin algebra?

I wonder if the triangulated category K(R-Mod) is compactly generated when R is an artin algebra? R-Mod denotes all left R-modules. I understand this would be true if R has finite …
3answers
1k views

### What is interesting/useful about big Witt Vectors?

p-typical Witt vectors are (among other things) a canonical way of associating to a perfect ring A of characteristic p a complete DVR of characteristic 0 with residue ring A genera …
2answers
1k views

### Galois theory and rational points on elliptic curves

I am in search of a concrete example [a concrete elliptic curve in Weierstrass form] of how Galois theory helps to find rational points on an elliptic curve. Chapter VI of Silverma …
0answers
382 views

### When should a moment polytope have “smooth” faces?

A codimension $d$ face of a polytope is called rationally smooth if it lies on only $d$ facets, because this is exactly the condition for the corresponding toric variety to have on …
1answer
341 views

### How to find examples of non-trival kernel of maps between Brauer groups Br(R) -> Br(K)

Background/Motivation: The facts about the Brauer groups I will be using are mainly in Chapter IV of Milne's book on Etale cohomology (unfortunately it was not in his online note). …
1answer
360 views

### What are the ‘standard’ applications of the duals of the adjoint functor theorems?

There are some 'standard' applications of the adjoint functor theorem (AFT) and the special adjoint functor theorem (SAFT), for example, the existence of a free $\tau$-algebra (wh …
2answers
446 views

### Must a Strong deformation retractible 3-manifold be homeomorphic to $\mathbb{R}^3$?

Assume $M$ is an open 3-manifold which can be deformation retracted to a point. Is it necessarily homeomorphic to $\mathbb R^3$? (I know Whitehead had an example which is contract …
2answers
281 views

### Infinite collection of elements of a number field with very similar annihilating polynomials

Hello all, let $n$ be an integer $\geq 2$ and let $\alpha$ be an algebraic number of degree $n$. Let $R$ be the ring of algebraic integers in ${\mathbb Q}(\alpha)$, and let $B$ be …
2answers
5k views

### Latex Template for a Popular Math Journal

Can anyone offer a Latex template for a popular mathematics journal? It is easy to prepare a template for a technical journal with simple page layout but what I am looking for is s …
3answers
658 views

### Two finite groups with the same identical relations?

An identical relation on a group G is a word w in Fr, the free group on r elements (for some r), such that evaluating w on any r-tuple of elements of G yields the identity (this ju …
3answers
288 views

### Chance of something being fixed [closed]

I'm fixing a software defect that occurs 1 in n test runs. If I want to know that the probability of it being fixed is >= p for some 0 <= p < 1, how many times, m, do I need …
1answer
200 views

### Network flow gadget

Given m units of flow from a source node, and several possible destinations, is there a network flow gadget to force the flow to use only one destination? That is, send all m units …
3answers
444 views

### Given an integer n and a finite extension K of Q , find a polynomial of degree n that is irreducible over K

Given a positive integer n and a finite extension $K$ of $\mathbb{Q}$, can one always find an irreducible polynomial in $K[x]$ of degree n? What if $n$ is prime? The natural appr …
3answers
416 views

### Can all G-connections on a Riemann surface X be induced by maps from X to G

There is the invariant Maurer–Cartan 1-form on a compact semi-simple Lie group G. So if we pull it back using a map from X to G then we get a G-connection on X. The question is, ca …
3answers
335 views

### Which method to apply to this problem?

I'm a programmer and I came a across an interesting problem. I'm sure there is a mathematical method or an algorithm to solve it, but I don't know where to start with the search no …

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