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 equiva …

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_{*}\ …

Hi I am creating an android app that will generate a cycling route for users using a route finder. I am trying to allow the user to either prefer distance or routes with cyclelane …

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 minima …

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 t …

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 o …

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\mat …

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 inters …

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 …

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 $ …

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 smoot …

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; v …

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 Proposi …

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 rel …

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 be …