user avatar
user avatar
user avatar
Jian
  • Member for 4 years, 11 months
  • Last seen this week
Stats
2,375
reputation
20k
reached
52
answers
51
questions
Loading…
About

some questions for myself.

1.https://math.stackexchange.com/questions/174595/classification-of-prime-ideals-of-mathbbzx

  1. the number of left maximal ideals of Artinian ring may be infinite question about semi-local ring and Artin ring.

  2. a story of the Koszul complex. Motivation for Koszul complex

  3. where we use the cocycle condition in Gluing sheaves. Details of gluing sheaves on a cover

  4. An intuitive approach to the Jordan Normal form.https://math.stackexchange.com/q/411845/453628

  5. bimodule structure in $\text{Ext}^i_R(M, N)$ when $R$ is commutative. How do I understand the module structure on Yoneda Ext?

  6. Serre quotient. Quotient of category of f.g. modules by subcategory

  7. Flat vs faithfully flat.https://math.stackexchange.com/questions/394654/example-of-a-flat-but-not-faithfully-flat-ring-extension

9.GL(n,R) is not connected, GL(n,C) is connected. What's an easy way to show that $GL(n,\mathbb C)$ is connected?
Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous?
How to show path-connectedness of $GL(n,\mathbb{C})$
How to prove $GL_n(\mathbb{C})$ has no subgroup with finite index?
When are finite-index subgroups of a Lie group closed? subgroup of a lie group with finite index is closed. Zariski topology,by GL(n,C) is open affine variety of M_n(C)=C^{n^2}. C^{n^2} is irreducible, hence GL(n,C) is irreducible and dense. Hence GL(n,C) is connected.

  1. graded free is stronger than free "Graded free" is stronger than "graded and free"? Global dimension and graded global dimension of a graded ring https://mathoverflow.net/q/369683/106580

  2. derived category of $\text{coh}\mathbb{P}^1$ and derived cat of Kronecker algebra. https://mathoverflow.net/q/285955/106580

  3. If $B$ is the Serre subcategory of the abelian category of $A$, then $\textbf{D}(B)\rightarrow \textbf{D}_B(A)$ maybe not be fully faithful. But this is true for bounded(Miyachi) https://mathoverflow.net/q/236245/106580 derived category of quotient category

  4. Why is an injective quasi-coherent sheaf's restriction to an open subset still an injective object? https://mathoverflow.net/q/6762/106580

  5. Finite generated filed extension is finite extension(Zariski's version of Nullstellensatz)Finitely generated algebraic field extensions are finite extensions?

  6. Why is the limit of $n^{1/n}$ is 1 How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?

  7. Radical of a ring VS radical of a module, when Rad(R)M=Rad(M)? Jacobson radical of a ring and radical of finitely generated $R$-module

  8. $\text{height}(I)+\text{dim}(R/I)=\text{dim}(R)$ for all ideal $I$ of $R$ iff $\text{height}(\mathfrak{p})+\text{dim}(R/\mathfrak{p})=\text{dim}(R)$ for all prime ideal $\mathfrak{p}$ of $R$. Does codimension equal height in complete local domains?

  9. Homogeneous localization and regularity

1
gold badge
7
silver badges
15
bronze badges
26
Score
48
Posts
47
Posts %
24
Score
52
Posts
50
Posts %
22
Score
29
Posts
28
Posts %
9
Score
8
Posts
8
Posts %
6
Score
11
Posts
11
Posts %
5
Score
23
Posts
22
Posts %
Top posts
View all questions and answers