bio | website | xs4all.nl/~wilberdk/home.html |
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Aug 23 |
comment |
What is the abutment filtration of the second spectral sequence of hypercohomology?
In some old notes I found the comment that this is much easier to understand when using the derived couples of Massey, rather than Cartan-Eilenberg resolutions. Just apply ${\bf R}T$ to the triangle $\oplus_n \tau_{\leq n-1}K\to \oplus_n \tau_{\leq n}K\to \oplus_n H^n(K)\to$. |
Aug 21 |
comment |
What is the abutment filtration of the second spectral sequence of hypercohomology?
One should not take the spectral sequence of a bicomplex as the template. This spectral sequence is just one (too particular) case of the spectral sequence of a filtered complex. One should take the spectral sequence of a filtered complex as the template. Look for a more relevant filtration of $\text{Tot}(L)$. |
Aug 20 |
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What is the abutment filtration of the second spectral sequence of hypercohomology?
Just like the naive truncation the canonical filtration can be understood as a filtration by subcomplexes. So we eventually end up with something that looks suspiciously like the spectral sequence for cohomology of a filtered complex. One must replace cohomology $H^n$ with ${\bf R}^nT$ in the theory for that spectral sequence. |
Jul 30 |
comment |
When is an exponential functor a bialgebra?
Did you read section 5 of arXiv:0902.4459 ? It may be related. |
Jul 21 |
revised |
GIT over integers
activated links |
Jul 20 |
revised |
GIT over integers
More general result |
Jul 19 |
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GIT over integers
One may expect it. By inverting a nonzero element one may first kill the $R$ torsion in $A$, then hope to kill the $R$ torsion in $H^1(G,A)$. One hopes that $H^1(G,A)$ is finitely generated as an $A^G$ module. But I only seem to know that when $R$ contains a field, cf. arXiv:1109.5822 |
Jul 19 |
comment |
GIT over integers
I am not sure what the question is. If your Dedekind domain $R$ is of finite characteristic $p$, then the result just amounts to the trivial fact that you kill $H^1$ when inverting $p$. Our result that you may kill $H^1$ by inverting some integer is of interest only when $R$ itself does not have this property that you may kill it that way. |
Jul 19 |
answered | GIT over integers |
Jun 19 |
comment |
About G-modules with good filtrations
One may also observe that the two definitions are equivalent for submodules of the injective hull of a finite dimensional module. The definition of Jantzen gets unpleasant only when multiplicities of weight spaces of $U$-fixed points become infinite. |
Jun 6 |
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An exact sequence which does not split
It seems that $f"$ must be injective and that $g"$ must be surjective. If there is a section of $(f',f")$ then use that $End(X)$ is local? |
Apr 22 |
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Frobenius splitting of affine flag varieties
Olivier Mathieu, Asterisque 159-160 (1988) is about applying Frobenius splittings in Kac-Moody context. |
Mar 21 |
awarded | Yearling |
Feb 26 |
comment |
Invariant theory of $SL_2$ over a field of positive characteristic
By power reductivity one knows at least that if $W$ comes from a module over $\Bbb Z$, as in the case of $S^dV$, then every generator of $R_W$ has a power that comes from an invariant in characteristic zero. |
Feb 25 |
comment |
Representations of $SL(2)$ in characteristic 2
And what do you mean by `the invariant theory'? Just the invariants in this module? (They are the same as predicted by Clebsch-Gordan.) |
Feb 23 |
revised |
Normalizer of SL_2(Z) in GL_2(R)
added 95 characters in body |
Feb 21 |
comment |
Normalizer of SL_2(Z) in GL_2(R)
I have now clarified in my answer what it is an answer to. |
Feb 21 |
revised |
Normalizer of SL_2(Z) in GL_2(R)
added 18 characters in body |
Feb 21 |
comment |
Normalizer of SL_2(Z) in GL_2(R)
Sorry, I was answering the question in the title, which is different from the question in the body. |
Feb 21 |
answered | Normalizer of SL_2(Z) in GL_2(R) |