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We prove that under suitable finiteness hypotheses, and assuming that p is invertible on X, the canonical functor e_p^comp: SH(X_et^hyp)_p^comp -> SH_et(X)_p^comp is an equivalence of infty-categories. The primary novelty of our argument is that we use the pro-etale topology to construct directly"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.08028","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-10-18T13:04:48Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2a72d7f4d0dee77cd52ee5d08b6c2bb3a47ac4627479f9c1ef94c6c59bb46637","abstract_canon_sha256":"d083f782b932a8a70ace6f0675c9f301b56e376021de58d58c11f4ccb2d1f50a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:47:11.499782Z","signature_b64":"dpYPPMe85asDxsy+1SWVclcVqFQYEjwg/2YVTX6lWy30NhYxL22wq+8lXZvGfNPOx6ZpVAVb4IccuQmANd3FCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23924f482d0d7e44f83a0a1d65f6c04308a24d389a1cdd42c9640ad48bbdbafe","last_reissued_at":"2026-07-05T03:47:11.499387Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:47:11.499387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity in etale motivic stable homotopy theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Tom Bachmann","submitted_at":"2018-10-18T13:04:48Z","abstract_excerpt":"For a scheme X, denote by SH(X_et^hyp) the stabilization of the hypercompletion of its etale infty-topos, and by SH_et(X) the localization of the stable motivic homotopy category SH(X) at the (desuspensions of) etale hypercovers. For a stable infty-category C, write C_p^comp for the p-completion of C. We prove that under suitable finiteness hypotheses, and assuming that p is invertible on X, the canonical functor e_p^comp: SH(X_et^hyp)_p^comp -> SH_et(X)_p^comp is an equivalence of infty-categories. 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