{"paper":{"title":"Relations between dynamical degrees, Weil's Riemann hypothesis and the standard conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Tuyen Trung Truong","submitted_at":"2016-11-03T18:43:28Z","abstract_excerpt":"Let $\\mathbb{K}$ be an algebraically closed field, $X$ a smooth projective variety over $\\mathbb{K}$ and $f:X\\rightarrow X$ a dominant regular morphism. Let $N^i(X)$ be the group of algebraic cycles modulo numerical equivalence. Let $\\chi (f)$ be the spectral radius of the pullback $f^*:H^*(X,\\mathbb{Q}_l)\\rightarrow H^*(X,\\mathbb{Q}_l)$ on $l$-adic cohomology groups, and $\\lambda (f)$ the spectral radius of the pullback $f^*:N^*(X)\\rightarrow N^*(X)$. We prove in this paper, by using consequences of Deligne's proof of Weil's Riemann hypothesis, that $\\chi (f)=\\lambda (f)$. This answers affirm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01124","kind":"arxiv","version":2},"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"}