Questions tagged [filtrations]
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43 questions
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Existence of raw versions for processes adapted to the augmented filtration
Let $(\Omega, \mathcal{F}, \mathbb{F}, \mathbb{P})$ be a filtered probability space with $\mathbb{F}=(\mathcal{F}_t)_{0\le t\le ∞}$.
Denote by $\mathcal{F}^{\mathbb{P}}$ the $\mathbb{P}$-completion of ...
- 155
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Associated graded of filtration which commutes with t-structure
Suppose that a filtration commutes with a t-structure: $F^p(\tau_{\leq n}K^\bullet)=\tau_{\leq n}(F^p K^\bullet)$, $F^p(\tau_{\geq n}K^\bullet)=\tau_{\geq n}(F^p K^\bullet)$. Then is it always true ...
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Coradical filtration for comodules is exhaustive
It is a standard fact in the theory of coalgebras and comodules that, given a coalgebra $C$ and a comodule $M$ over $C$, the coradical filtration
$$M_n := \Delta^{-1}(M\otimes C_0 + M_{n-1}\otimes C)$$...
- 558
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Literature request: Jordan-Hölder property in exact categories
The Jordan-Hölder theorem says that any chain of subobjects of a finite length object can be refined to a composition series, and that any composition series has the same length. We say an exact ...
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Characterizing filtrations generated by a stopping time
Setup
Let $\Omega$ be the set of càdlàg functions $f : [0,\infty) \to \mathbb R^d$ equipped with the Skorokhod topology for any $d \geq 1$, and let $X_t(\omega) = \omega(t)$ for any $\omega \in \Omega,...
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Normal bundle of veronese as iteration extension of symmetric powers
In this post, an answer claims that the normal bundle of the Veronese decomposes into a filtration, such that the associated graded is $$\bigoplus_{i=2}^d S^i T,$$ where $T$ is the tangent bundle. But ...
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Does weak convergence of filtrations preserve progressive measurability?
Suppose on some probability space $(\Omega, \mathcal{F}, \mathbb{P})$ I have a sequence of filtrations $\mathbb{F}^n =(\mathcal{F}^n_t)_{t \geq 0}$ generated by Brownian motions $W^n$ for each $n$, ...
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Maps from $\mathbb A^1/ \mathbb G_m$ to Coherent sheaves
I am reading this paper https://arxiv.org/abs/1608.04797
Let $\Theta$ be the stack $\mathbb A^1/{\mathbb G_m}$. Let $X$ be a smooth projective curve of genus $g$ over a field $k$. Let $Coh_P$ be the ...
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How to compute the integer corresponding to a class in $G_0(B_{\mathrm{red}})$ for a commutative noetherian ring $B$?
$\newcommand{\red}{\mathrm{red}}$Let $k$ be an algebraically closed field of characteristic zero and $m$ be a positive integer. Let $R$ be the subring $k[x,xy,xy^2,…,xy^m]$ of the polynomial ring $k[x,...
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Is every filtration on an abelian category strict?
It's well-known that the category of filtered objects in an abelian category is generally not an abelian category. One must generally add extra structure to ensure that all morphisms are strict for ...
- 16.2k
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Has anyone written about filtered Tannakian categories?
tl;dr Is there any source that discusses the concept of a filtered Tannakian category? I'm writing a paper with this notion and want to know if it's ever been discussed.
The original book by Saavedra-...
- 16.2k
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Filtration of norm-one elements of quaternion algebra over local field with respect to an involution
Let $K$ be a local non-archimedean field, with ring of integers $\mathcal{O}_K$, uniformizing element $\varpi_K$, and residue field $\mathcal{O}_K/\varpi_K\mathcal{O}_K \cong \mathbb{F}_q$. For ...
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When enlarging a filtration makes a stochastic processes into a solution to an SDE
Let $n$ be a positive integer and let $(Y_t)_{t\in [0,1]}$ on $\mathbb{R}^n$ be a stochastic process defined on a filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\in [0,1]},\mathbb{P}...
- 4,902
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Dimension of the associated graded module at an ideal
Let $I$ be an ideal of a Noetherian local ring $(R, \mathfrak m)$. Define the associated graded ring $G_I(R):=\bigoplus_{n=0}^\infty I^n/I^{n+1}$. Then $G_I(R)$ is a Noetherian ring of the same ...
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Properties of filtrations preserved by a DG-algebra homomorphism
Suppose we have a homomorphism $f : A^{\bullet} \longrightarrow B^{\bullet}$ of differential graded algebras over a field $k$, and consider the filtration
\begin{align*}
A^{\bullet} \supseteq F^0A^{\...
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