13 problems

Let $p$ be a prime, let $\operatorname{eo}_{p-1}$ be the proposed connective form of $EO_{p-1}$, and let $a_2,\dots,a_{p-1}$ be exterior generators with … Let…

Let $k$ be the base field and let ${\operatorname{{\mathcal S}{\mathcal H}}}_{S^1}(k)$ be the Morel–Voevodsky homotopy category of $S^1$-spectra. For an integer $d$, let…

Let $f:X\to\mathbf A^1$ be a function on a smooth complex algebraic variety, and let $x$ be a closed point of $f^{-1}(0)$. Suppose the singular locus of $f$ is a curve with local c…

Let $p$ be a prime, and let a spectrum of fp-type $n$ mean a bounded below, $p$-complete fp-spectrum whose associated thick subcategory of finite spectra has type at least $n+1$. L…

Vasil'ev–Grechkoseeva conjecture. Suppose that $L$ is one of the following nonabelian simple groups:

Meta-Isomorphism Conjecture. The induced map

Let $D_2$ be the little $2$-disks operad equipped with its $S^1$-action, let $\Sigma^\infty_+$ denote suspension spectrum after adjoining a disjoint basepoint, and let $K$ be the d…

Let $\tau$ be a nonzero element of $\pi_{k-1}(\mathbb{S}^0)$, and let $C\tau$ denote its cofiber. Mahowald's conjecture. The spectrum $C\tau$ does not admit an $A_{\infty}$-structu…

Let $\mathbb{S}=\Sigma^\infty S^0$ be the sphere spectrum, and let $\tau_{[0,n]}\mathbb{S}$ denote its truncation to degrees from $0$ through $n$. Let $\mathcal{F}_L^{(n)}$ be the…

The preceding constructions involve spectra $\mathbf L(i)\wedge \mathbf T(2^{n-i}-1)$, together with the spectra appearing in the complex of Theorem; the final cofibration has sourc…

Work at a prime $p$, and consider the connecting maps in the Taylor tower evaluated at ${\mathbb C}^0$: … A contracting homotopy for the complex of spectra ${\overline{M}}(k)$ woul…

Reduced $bu$ Whitehead conjecture. The complex is exact at the prime $p$.

$bu$ Whitehead conjecture. The complex is exact at the prime $p$.