7 problems

Hartl's local-system maximality conjecture. The space $\breve{\cal{F}}^0_b$ is the largest open $\breve E$-analytic subspace of $\breve{\cal{F}}^{wa}_b$ carrying a local system…

Hartl's connectedness conjecture. The space $\breve{\cal{F}}^0_b$ is arcwise connected.

Hartl's value-group conjecture. One has

Let $\mathcal M_4^{(1)}$ be the moduli space under consideration, let $\mathcal M_{\mathrm{Coble4}}^\circ$ be the open locus obtained from smooth stable Coble type quartics, and le…

Let $d4a4_2$, $d4a4_6$, $d4a4_8$, and $d4a4_d$ for $de5 16$ denote the indicated Heegner divisors, and call a Heegner divisor HLS if it has the HLS property used in the paper. HLS…

Banach cohomology and comparison conjecture. There is an isomorphism of topological $K$-vector spaces

Assume that $F$ has characteristic $0$ and that $\mu$ is minuscule. Let $G$ be the reductive group, let $b_0$ be the basic element associated with $(G,\{\mu\})$, and let…