1,007 reputation
218
bio website
location Hangzhou, China
age 22
visits member for 1 year, 10 months
seen Sep 1 at 19:31

I'm just a guy learning and enjoying in math. My name in MO is yizhongxunhuan. Which in Chinese means a recycle.


Aug
8
awarded  Altruist
Aug
7
awarded  Investor
Aug
7
comment Norm map over Galois extension
I can prove it if F is a finite field. But in general I guess it's not right and should have some counterexample. And I just can't find one...
Aug
7
comment if $K/F$ is a Galois extension, show that any intermediate field $L$ is generated by the traces of elements from $K$ over $L$.
@Alex Then you just check when is the trace of a normal basis generator, call it $\beta$, is fixed by an element in Gal(K/F). The answer is iff the element is actually in Gal(K/L). Then by the Fundamental Theorem in Galois Theory, we may conclude that F($\beta$)=L.
Aug
7
comment if $K/F$ is a Galois extension, show that any intermediate field $L$ is generated by the traces of elements from $K$ over $L$.
I think there is a typo. L should be generated by the traces of K over L with coefficients in F. So @MattE 's trick probably won't work here. As the case L=F is trivial...
Aug
5
comment To control first derivative with the function itself.
Sorry, but the inequality doesn't hold can't apply we have a inverse inequality. So I don't think you really solved this problem.
Aug
5
comment To control first derivative with the function itself.
@Siminore you are right, I missed C. And I edited it like 5 days ago, but as this site is blocked in China, I couldn't add comment to tell you guys. Sorry for my mistake. And I still can't solve this problem, neither did Manyfolds solve this problem.
Aug
5
comment A proof of the normal basis theorem of a cyclic extension field
@MakotoKato Could you tell me what's the proof that applies to both cases? I was asked to prove the normal basis theorem as a homework, but I really don't have any idea... Thanks a lot.
Jul
31
revised To control first derivative with the function itself.
added 2 characters in body
Jul
31
asked To control first derivative with the function itself.
Jul
2
awarded  Curious
May
26
awarded  Revival
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
Oh, BTW, the 2-dimensional case can be proved by Chern-Weil theory, as it is a well-known fact that all 2-real-dim'l Riemannian manifolds are Riemann surfaces.
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
I only know that the Chern-Weil theory will give the G-B-C theorem for complex manifolds. The way I know to get Pfaffian is that from Mathai-Quillen's geometric construction of Thom classes.
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
It seems hard to get Pfaffian from Chern-Weil theory? Isn't Chern-Weil assume the bundle tobe complex vector bundle, and I think the tangent bundle of arbitrary real manifold won't admit a complex vector bundle structure.
May
13
asked Two books defined two Chern(Euler) classes yet differed by a negative sign, what's wrong?
Mar
28
accepted How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$?
Mar
23
accepted Total mean curvature of an immersed torus.
Mar
21
accepted Is every separately continuous function on $R^2$ continuous?
Mar
20
asked Is every separately continuous function on $R^2$ continuous?