{"paper":{"title":"Construction of Anti-Cyclotomic Euler Systems of Abelian Varieties Associated to $X_1(N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Heon Kim, Daeyeol Jeon. Byoung Du Kim","submitted_at":"2017-10-25T01:51:38Z","abstract_excerpt":"Let $K$ be an imaginary quadratic field, $N$ be a positive integer, $f(z)$ be a newform of level $\\Gamma_1(N)$, and $A_f$ be the abelian variety associated to $f$. For each $\\tau \\in K$ ($\\operatorname{Im} \\tau >0$), we construct a certain point $P_\\tau$ on $A_f$ defined over an extended ring class field of $K$ of level $N$. Our construction generalizes Birch's construction of the Heegner points to the abelian varieties associated to modular forms of level $\\Gamma_1(N)$ and nontrivial character. Then, we show that $P_\\tau$'s satisfy the distribution and congruence relations of an Euler system,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09043","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}