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arXiv · 2308.10736

Syntomic complex and $p$-adic nearby cycles

Abhinandan
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Abstract

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the associated $F$-isocrystal. In global applications, for smooth ($p$-adic formal) schemes, we establish a comparison between the syntomic complex with coefficients in a locally free Fontaine--Laffaille module and the $p$-adic nearby cycles of the associated \'etale local system on the (rigid) generic fibre.

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Abhinandan. 2023-08-21. Syntomic complex and $p$-adic nearby cycles. https://doi.org/10.2140/ant.2026.20.17

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