9
votes
2answers
503 views

Is the Characteristic of a Field Detectable from the Topology of a Topological Vector Space?

Motivation A topological vector space is a vector space over a (topological) field, K, that carries a topology such that addition and scalar multiplication are continuous maps, e.g., all normed ...
4
votes
0answers
328 views

Given two linear operators A and B over a finite field, is there a third operator C whose kernel is the intersection of kernels of A and B?

Let $V$ be a finite dimensional linear space over a finite field $k$. Let $A$ and $B$ be two endomorphisms of $V$. Question 1. Is there an endomorphism $C$ of $V$, which is expressed in terms of ...
5
votes
3answers
882 views

Is $Sym^n (V^*) \cong Sym^n (V)^\ast$ naturally in positive characteristic?

Background/motivation It is a classical fact that we have a natural isomorphism $Sym^n (V^*) \cong Sym^n (V) ^\ast$ for vector spaces $V$ over a field $k$ of characteristic 0. One way to see this is ...