The weights tag has no wiki summary.
6
votes
2answers
310 views
Hodge structure versus Weight structure
This is a naive question.
One is told that, somehow, Hodge theory for varieties over complex numbers, is an analog of weight theory for varities over finite fields. In weight theory, one considers ...
2
votes
0answers
80 views
Groups of automorphisms of weighted graphs
Let $\Gamma=(V,E,\omega)$ be an (edge-)weighted graph without loops and multiple edges. Here $V$ is the set of vertices, $E$ is the set of edges and $\omega:E \to \mathbb{N}$. A permutation $\varphi$ ...
3
votes
0answers
194 views
Tiling a rectangle with weighted cells (min-max problem)
I have been struggling with a research problem. The problem can be formalized as follows:
Given a $n\times m$ matrix $A$ containing cells with non-negative integer values, partition it in $J$ ...
0
votes
0answers
92 views
Ratio of weighted sums => weighted sum?
Is it possible to convert a ratio of weighted sums to one single weighted sum whose weights depend on the previous weights?
Let $m_1,m_2,m_3...$ and $n_1,n_2,n_3...$ be weights. This is the ratio of ...
10
votes
2answers
339 views
A_infinity structure on cohomology and the weight filtration
Let $X$ be a complex algebraic variety. The rational cohomology of $X(\mathbb{C})$ carries a canonical filtration called the weight filtration. It also carries a canonical equivalence class of ...
0
votes
0answers
43 views
semicontinuity results for weights
Let $f:X\rightarrow Y$ a proper flat map between smooth schemes over a finite field $k$ and the base is integral.
For an integer $i$, we consider the the l-adic sheaf $R^{i}f_{*}\mathbb{Q_l}$ and
...
4
votes
2answers
276 views
Weights of restricted modules of some Cartan type Lie algebras
Let $L$ be a simple Lie algebra of Cartan type of absolute toral rank 2 over an algebraically closed field $\mathbb{F}$ of characteristic $p\geq 5$.
Denote by $L_{[p]} $ the minimal $p$-envelope of ...
1
vote
0answers
147 views
Universal Correlation measure — ranking correlations
I have time series data of experimental observations for two related processes. I want to measure correlation for use in further analysis.
Correlation of the series changes over time and across ...
1
vote
1answer
81 views
weighted to centre mean
I'm not even sure if what I want to do is a good idea but I figure I'll experiment and see.
I have two predicted ratings in the range of 1-5 based on two different algorithms for predicting movie ...
2
votes
1answer
321 views
Which (reducible) projective varieties could be presented as 'relatively smooth' hyperplane sections of irreducible (normal) ones?
Are there any restrictions known on a (complex reducible) projective variety $Y$ that can be presented as $Z\cap H$, where $Z$ is a normal (or just irreducible) closed subvariety of a smooth ...
1
vote
0answers
121 views
A Weyl invariance constructed from Clebsch-Gordan Coefficients.
Let $V$ and $\tilde{V}$ be irreducible representations of SU(N) with tensor decomposition:
\begin{equation}
V \otimes \tilde{V} = \bigoplus_i U_i
\end{equation}
\noindent were $U_i$ are also irreps ...
2
votes
0answers
220 views
Does Artin's vanishing hold for '$E_2$-weight pieces' for (torsion) cohomology of affine varieties?
Let $X$ be an affine variety of dimension $n$ (say, over complex numbers). Then Artin's vanishing theorem yields: both singular and etale cohomology $H^i(X):=H^i(X,\mathbb{Z}/l\mathbb{Z})=0$ for ...
6
votes
1answer
371 views
Does intersection pairing on `$IH^*(X)$` agree with cup-product on `$H^*(X)$`?
Let $X$ be a proper singular variety over $k=\overline{\mathbb F}_p,$ irreducible of dimension $d.$ Let $H^*(X)$ and $IH^*(X)$ be the $l$-adic cohomology groups and $l$-adic intersection cohomology ...
5
votes
4answers
438 views
Smooth in codimension-k and the weight filtration
Let $X$ be an algebraic variety. Then $H_{et}^k(X)$ has a filtration whose associated graded pieces are labeled by "weights", certain integers between $0$ and $2k$. If $X$ is smooth, then the weights ...
1
vote
2answers
205 views
Maximizing the ratio of (weigthed sum)/sqrt(variance_weighted_sum)
I have a weighted sum,
weighted sum = w1*mu1 + (1-w1)*mu2
with
variance weighted sum = (w1^2)*var1 + ((1-w1)^2)*var2 + 2*w1*(1-w1)*cov
in which
mu1 = mean 1;
mu2 = mean 2;
var1 = variance for ...
2
votes
0answers
158 views
A Hodge substructure with ''nice' weight factors that does not correspond to a mixed submotif?
Suppose that we have a mixed motif $M$ with only two (subsequent) weights, and have a subobject for each weight factor. How we can control whether there exists a submotif of $M$ with these two ...
3
votes
1answer
623 views
Do Deligne's decalage and two filtrations for mixed Hodge complexes have a conceptual explanation?
As far as I understood, there are two way to assign weights to a mixed Hodge complex (a way that does not depend on shifts, and another one that does). There is a clever way to relate these to ways ...
6
votes
0answers
263 views
Cohomology of Zariski neighborhoods
Do there exist smooth compact (=complete) connected complex algebraic varieties $X\subset Y$ and a Zariski neighborhood $U$ of $X$ in $Y$ such that the image of $H^{\ast}(U,\mathbf{Z})$ in ...
7
votes
2answers
563 views
Which statements in section 5 of BBD will fail if we consider $\mathbb{Q}_l$-adic sheaves there?
A stupid question: which statements in section 5 of BBD will fail if we replace $\overline{\mathbb{Q}_l}$-sheaves by just $\mathbb{Q}_l$-ones? I am especially interested in Proposition 5.1.15.
BBD = ...
4
votes
2answers
567 views
In what setting does one usually define mixed sheaves and weights for them?
In BBD mixed sheaves and weights for them were only defined for ($\overline{\mathbb{Q}_l}$-)sheaves over a variety $X_0$ defined over a finite field $F$. Weights start to behave better when one ...
