{"paper":{"title":"Non-commutative twisted Euler characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Somnath Jha, Sudhanshu Shekhar","submitted_at":"2017-10-11T10:07:48Z","abstract_excerpt":"It is well known that given a finitely generated torsion module $M$ over the Iwasawa algebra $\\mathbb Z_p[[\\Gamma]]$, where $\\Gamma \\cong \\mathbb Z_p$, there exists a continuous $p$-adic character $\\rho$ of $\\Gamma$ such that, for the twist $M(\\rho)$ of $M$, the $\\Gamma_n := \\Gamma^{p^n}$ Euler characteristic, i.e. $\\chi(\\Gamma_n, M(\\rho))$, is finite for every $n$. We prove a generalization of this result by considering modules over the Iwasawa algebra of a general $p$-adic Lie group $G$, instead of $\\Gamma$. We relate this twisted Euler characteristic to the evaluation of the {\\it Akashi ser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03985","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"}