4,284 reputation
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bio website nullteilerfrei.de
location Germany
age 29
visits member for 3 years, 6 months
seen 1 hour ago

I'm a PhD student with research interests in Algebraic Geometry, Algebraic Complexity Theory and Geometric Invariant Theory.


Nov
17
answered Vector space and algebraic closure of a field
Nov
17
revised Representation theory of the general linear group over a finite prime field
added 202 characters in body
Nov
4
answered Is $K[x,y,z,\frac{1}{xz}]$ an integral domain?
Oct
31
comment Representation theory of the general linear group over a finite prime field
I am perfectly sure what the question is, it is the one written up there. I just do not know what your definition of a representations of the algebraic group $\operatorname{GL}_n/\mathbb F_p$ is. @Stephen, you are correct.
Oct
31
comment Representation theory of the general linear group over a finite prime field
@Thomas: Most definitely not, everything is over $\mathbb F_p$.
Oct
31
comment Representation theory of the general linear group over a finite prime field
I worded my question more cautiously. I am not sure if I want the representations of the algebraic group $\operatorname{GL}_n/\mathbb F_p$, in case that somehow involves the algebraic closure of $\mathbb F_p$, I am indeed looking at the finite group $\operatorname{GL}_n(\mathbb F_p)$ acting on $\mathbb F_p$-vector spaces.
Oct
31
revised Representation theory of the general linear group over a finite prime field
added 167 characters in body
Oct
31
asked Representation theory of the general linear group over a finite prime field
Oct
28
answered All the $k\times k$ minors determines the matrix?
Oct
23
comment Worst-case time to copy one movie
For $N=99$ you'd only have $H_1$ and $H_2$ because $\log_{10}(N+1)=\log_{10}(100)=2$.
Oct
22
revised Rational functions on varieties
added 6 characters in body
Oct
21
answered Reference request for algebraic Peter-Weyl theorem?
Oct
17
comment UFD and relatively prime elements
You are not quite sincere, there is a hint in the book: It says that $\gamma$ is the resultant of $u$ and $v$. The fact he states is a known property of resultants.
Oct
17
answered A question about Klaus Hulek algebraic geometry (regarding Noether normalization)
Oct
15
comment Divisibility of polynomials in a subfield of a field.
+1 and yes, I admit I chose an easy path.
Oct
15
answered Why $\mathbb Z/ 2 \mathbb Z$ is not a free module?
Oct
15
answered Divisibility of polynomials in a subfield of a field.
Oct
11
comment Is a coherent locally free sheaf isomorphic it's dual?
No, a locally free sheaf is not in general isomorphic to its dual, not even in the very special case of line bundles. Here, the dual $\mathcal L^\ast$ of a line bundle $\mathcal L$ serves as an inverse to $\mathcal L$ in the Picard group. This might be a good case to study to understand what's going on.
Oct
5
comment Why is the multiplicative subgroup of a field an affine algebraic group?
No, I am relying on the fact that (2) is true. They are isomorphic as varieties and the group structure on $G_m$ induces a group structure on the hyperbola via this exact isomorphism.
Oct
4
comment Why is the multiplicative subgroup of a field an affine algebraic group?
Regarding 1), you just gave the description in the sentence before: Take $n=2$ and observe that $f=x_1x_2-1$ is irreducible. The ideal generated by $f$ is a prime ideal in $K[x_1,x_2]$ and its zero locus is (isomorphic to) the multiplicative group. Regarding 2), simply consider the projection $K\times K\to K$. You should be able to show that the restriction to $G$ is injective and has image $G_m$.