6 problems

Eisenstein quotient conjecture. The map $\widetilde{\varpi}_{G'}$ factors through the Eisenstein ideal, and $\varpi_{G'}$ induces an isomorphism

Let $N$ be the prime level and $p$ a prime with $p\nmid N$. Let $H_+$ be the plus part of the modular-symbol homology group, let $I$ be the Eisenstein ideal acting on $H_+$, let…

Let $(p,j)$ be an irregular pair satisfying the Gorenstein conditions, let $\mathcal{T}^c_{\mathfrak m^c}$ be the corresponding localized cuspidal Hecke algebra, and let…

Let $L$ be the set of supersingular lambda invariants, let $M'$ be the free module generated by the symbols $[\lambda]$ for $\lambda\in L$, and let $e_0^0$ and $e_0^1$ be the eleme…

Rank–order conjecture. The following are equivalent:

For $N\geq 1$, Manin symbols in the relative homology group $H_1(X_1(N),\{\mathrm{cusps}\},\mathbb{Z})$ map to Steinberg symbols in $K_2(\mathbb{Z}[\zeta_N,\tfrac{1}{N}])$, relatin…