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Sep
29
comment Multiprecision numerical evaluation of integral: Sage vs. PARI/GP vs. mpmath
Indeed the WorkingPrecision->50 should simply be deleted. One should leave that to Mathematica. And tau should not have been made numerical.
Sep
24
awarded  Autobiographer
Sep
18
comment F-splitting and F-purity from commutative algebra viewpoint
See my expository paper (arxiv.org/a/vanderkallen_w_1) Frobenius Splittings
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
comment 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
comment 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
comment 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
comment 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.