22 problems

Let $G$ be a finite group and let a local $G$-action be an embedding $\rho:G\hookrightarrow\operatorname{Aut}(k[[t]])$, where $k$ is algebraically closed of characteristic $p>0$. T…

Bloch's semiregularity conjecture. The map $\tau$ annihilates all obstructions, giving a reduced obstruction space.

The compatibility conjecture. The isomorphism $\eta$ induces an isomorphism of perfect obstruction theories

Obstructed semi-manifold obstruction conjecture. Obstructed semi-manifolds may have nonvanishing ordinary obstruction, and this obstruction can be calculated by extending standard…

Let $R$ be an even commutative $S$-algebra, let $x\in R_d$, and let $p$ be a prime such that $n$ is invertible in $R_*$ for every $n<p$. Let $\bar c_n(x)\in\pi_{p(d+2)-2}R/(p,x)$ d…

Let $R$ be an even commutative $S$-algebra, let $x\in\pi_dR$ be a nonzero divisor, and consider the quotient $R/x$. An $A_\infty$ multiplication is a homotopy-coherent associative…

Let $X$ be a closed manifold of dimension $n$ whose relevant connectivity or cohomological parameter is denoted by $r$, and let Theorem 1(1) assert the result under the bound…

Let $\mathcal{F}$ and $\mathcal{G}$ be flow categories, and let $\mathcal{W}:\mathcal{F}\to\mathcal{G}$ be a $\tau_{\leq n}$-morphism. The paper proves the obstruction criterion wh…

Let $D_q$ be a dihedral group acting locally over an algebraically closed field $k$ of characteristic $p>0$. Assume that the KGB obstruction for this action vanishes. Dihedral KGB-…

Let $X$ be a Calabi-Yau $4$-fold and $S\subseteq X$ a local complete intersection surface. For an extension of local Artinian schemes…

The free-starting-positions obstruction conjecture. Every such affine line $\mathcal L$ intersects infinitely many of these hypercubes. This is an obstruction-theoretic equivalent…

Let $X$ be a smooth projective variety over a field $k$ of characteristic zero, and let $Y\subset X$ be a closed locally complete intersection subvariety of codimension $p$. Let…

Superpotential conjecture. The obstruction theory of any holomorphic object on a Calabi–Yau manifold should be governed by a superpotential.

Massey obstruction conjecture. These cohomology classes are obstructions to lifting $\widetilde f_4$ to a map

Higher obstruction equivalence conjecture. Such data determines a point in

Let $L_\infty$ be the limiting linear map appearing in the desingularization and obstruction setup, where the theorem was originally stated under the assumption…

Compatibility conjecture. The restriction $\iota_{n,\alpha}^*{\mathbb E}$ agrees, as a symmetric perfect obstruction theory, with ${\mathbb E}_{\operatorname{crit}}$.

Let $(X,T^*_{X,-})$ be a model and let $(Y,T^*_{Y,-})$ be a $gt$-model over a connected Stein base whose fiber is $(X,T^*_{X,-})$, so that $Y=X\times B$ and…

Let $(Y,T^*_{Y,-})$ be a $gt$-model. The secondary obstruction complex has differentials … Let $\Theta(T^*_{Y,-})$ denote the model class and let…

The paper constructs an extended spectral sequence using cofiber sequences of differential graded operads and compares its range with Bousfield's extension for towers of fibrations…

For an integer $n$, consider $n$-dimensional cell complexes $K$ whose underlying spaces are $(n-1)$-connected and do not embed in $S^{2n}$. An $h$-minor is a cell complex obtained…

Homotopy-classification conjecture. There are maps $W,W'$ and an action $b$ such that the following sequence of sets is exact: