{"paper":{"title":"Cokernels of restriction maps and subgroups of norm one, with applications to quadratic Galois coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cristian D. Gonzalez-Aviles","submitted_at":"2018-04-04T18:19:09Z","abstract_excerpt":"Let f: S' --> S be a finite and faithfully flat morphism of locally noetherian schemes of constant rank n and let G be a smooth, commutative and quasi-projective S-group scheme with connected fibers. For every r>0, let Res_{G}^{(r)}: H^{r}(S_{et},G)---> H^{r}(S'_{et},G) and Cores_{G}^{(r)}: H^{r}(S'_{et},G)---> H^{r}(S_{et},G) be, respectively, the restriction and corestriction maps in etale cohomology induced by f. For certain pairs (f, G), we construct maps \\alpha_{r}: Ker Cores_{G}^{(r)}---> Coker Res_{G}^{(r)} and \\beta_{r}: Coker Res_{G}^{(r)}---> Ker Cores_{G}^{(r)} such that \\alpha_{r}o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01553","kind":"arxiv","version":3},"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"}