In algebraic geometry, an ℓ-adic sheaf on a Noetherian scheme X is an inverse system consisting of Z / ℓ n {\displaystyle \mathbb {Z} /\ell ^{n}} -modules F n {\displaystyle F_{n}} in the étale topology and F n + 1 → F n {\displaystyle F_{n+1}\to F_{n}} inducing F n + 1 ⊗ Z / ℓ n + 1 Z / ℓ n → ≃ F n {\displaystyle F_{n+1}\otimes _{\mathbb {Z} /\ell ^{n+1}}\mathbb {Z} /\ell ^{n}{\overset {\simeq }{\to }}F_{n}} . Bhatt–Scholze's pro-étale topology gives an alternative approach.
In algebraic geometry, an ℓ-adic sheaf on a Noetherian scheme X is an inverse system consisting of Z / ℓ n {\displaystyle \mathbb {Z} /\ell ^{n}} -modules F n {\displaystyle F_{n}} in the étale topology and F n + 1 → F n {\displaystyle F_{n+1}\to F_{n}} inducing F n + 1 ⊗ Z / ℓ n + 1 Z / ℓ n → ≃ F n {\displaystyle F_{n+1}\otimes _{\mathbb {Z} /\ell ^{n+1}}\mathbb {Z} /\ell ^{n}{\overset {\simeq }{\to }}F_{n}} . Bhatt–Scholze's pro-étale topology gives an alternative approach.
Source: Wikipedia "ℓ-adic sheaf" · CC BY-SA 4.0
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