{"paper":{"title":"Tensor and convolution direct image of $\\ell$-adic sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Antonio Rojas-Le\\'on","submitted_at":"2018-06-07T16:48:42Z","abstract_excerpt":"Given a Galois \\'etale map of varieties $\\pi:Y\\to X$ and an $\\ell$-adic sheaf or derived category object $P\\in D^b_c(Y,{\\mathbb Q}_\\ell)$, we study two cohomological operations: the tensor direct image and (in the case of perverse sheaves) the convolution direct image, which give objects of $D^b_c(X,{\\mathbb Q}_\\ell)$, and can be used to improve the estimates on some partial exponential sums and the number of rational points on certain varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02777","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"}