{"paper":{"title":"The norm map and the capitulation kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Cristian D. Gonzalez-Aviles","submitted_at":"2018-03-09T15:46:42Z","abstract_excerpt":"Let f: S'--> S be a finite and faithfully flat morphism of locally noetherian schemes of constant rank n > 1 and let G be a smooth, commutative and quasi-projective S-group scheme with connected fibers. Under certain restrictions on f and G, we relate the kernel of the restriction map in degree r>0 \\'etale cohomology Res_{G}^{(r)}: H^{r}(S_{\\et},G)--> H^{r}(S'_{\\et},G) to a certain quotient of the kernel of the mod n corestriction map in degree r-1, namely Cores_{G}^{(r-1)}/n: H^{r-1}(S'_{\\et},G)/n\\to H^{r-1}\\lbe(S_{\\et},G)/n. When r=1 and f is a Galois covering with Galois group D, our main t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03574","kind":"arxiv","version":4},"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"}