6 problems

Let $\Pi_{17}$ be the double cover of the Teichmüller curve $W_{17}\hookrightarrow\mathbb{H}^2/\mathrm{SL}(\mathcal{O}_{17}\oplus\mathcal{O}^{\vee}_{17})$. For $j\in\{1,2\}$ and ev…

Ogus' principle. Assume that the conjugacy class of $\mu$ is defined over $\mathbf{F}_p$. For every $x\in S_K(k)$,

Let $p>3$ be prime, let $l\equiv p-1\pmod p$ be prime, and let $E_p$ be the Tate normal form for a point of order $p$. Write $\hat H_{p,l}(x)$ for its Hasse invariant over…

Let $l\neq 2,3,7$ be a prime. Let $\hat H_{7,l}(x)$ denote the Hasse invariant polynomial of the Tate normal form $E_7$ over $\mathbb F_l$, and let $h(-l)$ denote the relevant clas…

Diamond's conjecture. The cone $C_X$ is equal to the cone spanned by the weights of Goren's partial Hasse invariants.

Let $G$ be a reductive group defined over $cF_q$ with a Borel pair $(B,T)$ defined over $cF_q$. Let $P$ be a parabolic subgroup containing $B^{-}$, set $Q:=csigma(P^{-})$, and let…