37 problems

Let $F$ be an infinite field, let $\overline{\mathcal{L}^{\mathrm{f}}}(F)=\mathcal{L}^{\mathrm{f}}(F)/\mathcal{L}^{\mathrm{f}}_1(F)$, and let $\overline{\delta}^{[k]}$ be the $k$-f…

Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$ with non-trivial valuation, let $M$ be a finite free differential module over $K[\![t]\!]_0$ admittin…

Let $\{\mathfrak L_\alpha\}_{\alpha\in[0,1]}$ be the filtration of $\mathcal G_0$ defined in the paper. The family is called strict when its inclusions are strict as the parameter…

Assume that the characteristic exponent $p$ is inverted and take the étale topology. For every smooth $k$-variety $X$, write $h_0^{\text{\scriptsize{\rm {\'e}t}}}(X)$ for its zerot…

Let $p<p'$ be relatively prime positive integers, set $t=p'/p$ with $1<t<2$, and let $M_{r,s}^{(p,p')}$ be the irreducible Virasoro module with $1\le r<p$ and $1\le s<p'$. For allo…

Let $X$ be a smooth real projective variety. Let $RT_tH_n(X)$ denote the topological filtration on $H_n(ReX;\mathbb Z_2)$, given by the image of $\Phi_{t,n}$, and let $RG_tH_n(X)$…

Let $\hat {\cal B}_{m}^{\,u}$ be the diagram space equipped with the filtration whose quotient at $(f,o,e)$ is ${\cal G}_{f,o,e}^{\,}\,\hat {\cal B}_{m}^{\,u}$. Let $T(m,u)$ be the…

Separatedness and motivic identification conjecture. The filtration $F_{\mathcal{M}}$ is separated and gives the conjectural motivic filtration of Beilinson and Bloch.

Let $W(k)$ be the Witt ring of quadratic forms over a field $k$, with $I\subset W(k)$ the ideal of even-dimensional forms. For an element $x\in W(k)$, let its degree be the natural…

Let $X$ be an abelian surface, let $K_n(X)$ be the generalized Kummer variety, and let $z=\{z_0,\ldots,z_n\}\in K_n(X)$ with $z_m\in X$. For a point $z$, let $O_z$ denote its ratio…

Let $(X,\alpha)$ be a twisted abelian surface, let $K=K_\sigma(X,\alpha,\mathbf{v})$ be the kernel of the Albanese map, and suppose that $\dim K=2n$. For $E\in K$, let $O_E$ denote…

Roé-Urbinati's conjecture. The valuation $v$ is b-divisorial if and only if

Goodness conjecture. This trial filtration is good, in the sense reviewed in the source.

Let $M_A(\lambda,\eta)$ be a deformed standard Whittaker module over $A=\mathcal{O}(\mathbb{C}\gamma)_{(s)}$, and let $M(\lambda,\eta)$ denote its specialization at $s=0$. The Jant…

Let $(R,\mathfrak{m})$ be a Noetherian local ring, let $I$ be an $\mathfrak{m}$-primary ideal, and let $\mathcal{A}$ be an $I$-good filtration. Vasconcelos' uniformity conjecture.…

Let $\mathfrak G^{(0)}=\{\mathfrak G^{(0)}_\alpha\}_{\alpha\in[\alpha_*,1]}$ be the generalized filtration, and let $f\in\mathfrak G^{(0)}_\alpha$. The function $f$ generates a sem…

Boundary conjecture. The function $f$ belongs to $\partial\mathfrak H_\alpha$ whenever $\alpha\in(0,2/3]$. The source notes that several other boundary functions are known, while t…

Let $\mathfrak A=\{\mathfrak A_\alpha\}_{\alpha\le1}$ be the analytic filtration, and let $F_\alpha$ denote the function used in its definition. For each $\alpha\le1$, consider the…

Weight–stable-rank comparison conjecture.

Pour un corps $F$, soit $D_k\mathcal{C}(F)$ la filtration croissante par la profondeur, définie par $D_{-1}\mathcal{C}(F)=0$, $D_0\mathcal{C}(F)=\mathcal{C}_1(F)$ et la condition s…

Let $X$) be a separable Banach space. For integers $N,M\geq 0$, let $(f_{n,m}:0\leq n\leq N,0\leq m\leq M)$ be an $X$-valued martingale on $(\Omega,\mathcal{F},\mathbb{P})$ with re…

Decomposition conjecture. Any finite honest time can be expressed as the maximum of a finite honest time from a continuous filtration and a finite honest time from a discrete/jumpi…

Consider a graph providing an adic realization of an automorphism with positive entropy, together with its associated limiting simplex. Positive-entropy adic graph conjecture. Such…

Let $c4$ and $c4'$ be finitely isomorphic ergodic filtrations. Assume that both filtrations are nonstandard and that both have virtual matrix distributions for the sequences of ass…

The discussion concerns filtrations whose finite levels are isomorphic and whose associated sequences of semimetric spaces may admit an asymptotic comparison. Filtration isomorphis…