6 problems

Codominant-support conjecture. The local system $L_{z,w}^{J',\emptyset}$ is zero for every non-codominant permutation $z$. The conjecture would restrict the decomposition-theorem s…

Lagrangian-fibration conjecture. The morphism $f$ admits a multiplicative decomposition theorem

Corti–Hanamura's motivic decomposition conjecture. Every such morphism admits a motivic decomposition.

Let $\pi_M:(M,\sigma)\to B$ be an integrable system, with partial Fourier–Mukai transform $\phi_{\mathrm{FM}}$, sheaf of Kähler differentials $\Omega_M^k$, and decomposition-theore…

Let $K/\mathbf{Q}_p$ be a finite extension, and let $f:X\to Y$ be a projective map of rigid spaces over $K$ with $Y$ qcqs. Let $\mathrm{IC}_{X,\mathbf{Q}_\ell}$ be the intersection…

Let $X$ be a smooth complex algebraic variety, and let $\mathcal{M}_B(X)$ be the moduli space of semisimple local systems of all ranks. An absolute $K$-constructible set is a subse…