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In this talk, we will reconstruct de Rham cohomology by introducing a so-called de Rham space over the stack ([ \mathbb{A}^1 / \mathbb{G}_m ]), whose cohomology encodes the Hodge filtration. Its restriction to the closed point (B\mathbb{G}_m) recovers the Hodge decomposition, while its restriction to the open substack (\mathbb{G}_m / \mathbb{G}_m) recovers the full de Rham cohomology.

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