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Integral p-adic Hodge theory - announcement
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🧮 math.AG
math.NT
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cohomologyadicannouncementcrystallineetalefibretheorytorsion-free
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Given a proper, smooth (formal) scheme over the ring of integers of $\mathbb C_p$, we prove that if the crystalline cohomology of its special fibre is torsion-free then the $p$-adic \'etale cohomology of its generic fibre is also torsion-free. In this announcement we sketch the proof, which relies on the construction of a new cohomology theory interpolating between crystalline and \'etale cohomology. Further details and results, including a comparison isomorphism, will be presented in the full forthcoming article.
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