{"paper":{"title":"Geometric monodromy -- semisimplicity and maximality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"Akio Tamagawa, Anna Cadoret, Chun Yin Hui","submitted_at":"2017-02-22T21:48:16Z","abstract_excerpt":"Let $X$ be a connected scheme, smooth and separated over an algebraically closed field $k$ of characteristic $p\\geq 0$, let $f:Y\\rightarrow X$ be a smooth proper morphism and $x$ a geometric point on $X$. We prove that the tensor invariants of bounded length $\\leq d$ of $\\pi_1(X,x)$ acting on the \\'etale cohomology groups $H^*(Y_x,F_\\ell)$ are the reduction modulo-$\\ell$ of those of $\\pi_1(X,x)$ acting on $H^*(Y_x,Z_\\ell)$ for $\\ell$ greater than a constant depending only on $f:Y\\rightarrow X$, $d$. We apply this result to show that the geometric variant with $F_\\ell$-coefficients of the Groth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07017","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"}