Cohomological connectedness conjecture for the mixed elliptic motive algebra

Let $E$ be the elliptic curve and let ${\mathcal A}_{{\frak M}(E)}$ denote the algebra of mixed elliptic motives considered in the paper, graded by $i$. Cohomological connectedness conjecture. ${\mathcal A}_{{\frak M}(E)}$ is cohomologically connected with respect to $i$. This is motivated by viewing the relevant motivic cohomology groups as $E_2$-terms in a Leray spectral sequence, where cohomology vanishes in negative degrees. The conjecture is presented as a strengthening of the Beilinson–Soulé conjecture and is used to obtain a minimal-model description.