9 problems

Nestedness Conjecture. The stratification is nested: there is a partial order on the index set $\{\alpha\}$ such that

Epsilon-class conjecture. If $\nabla$ is an integrable, admissible, absolute connection, then

Determinant de Rham formula.

André's nilpotency conjecture. Then $(V,\nabla)$ is motivic.

Periodic de Rham conjecture. Any irreducible periodic de Rham bundle over $U$ is motivic.

Let the de Rham moduli space $\mathbb{M}_{\mathrm{dR}}(X,r)$ be equipped with its oper stratification, whose strata are indexed by $\alpha$. Oper Stratum Conjecture. The oper strat…

Let $\mathbb{S}_\alpha\rightarrow V_\alpha$ be the projections associated with the oper stratification of the de Rham moduli space. Foliation Conjecture. The Lagrangian fibers of t…

Let $K$ be a finitely generated field of characteristic zero, let $C$ be a curve over $K$, and let $(\mathscr{E},\nabla)$ be a vector bundle with connection on $C$. Choose an embed…

Semisimple monodromy conjecture. If almost all $p$-curvatures of $(V,\nabla)$ vanish, then $(V,\nabla)$ has semisimple monodromy.