A conjecture recently stated by Flach and Morin relates the action of the monodromy on the Galois invariant part of the p-adic Beilinson–Hyodo–Kato cohomology of the generic fiber of a scheme defined over a DVR of mixed characteristic to (the cohomology of) its special fiber. We prove the conjecture in the case that the special fiber of the given arithmetic scheme is also a fiber of a geometric family over a curve in positive characteristic.
A conjecture of Flach and Morin
Chiarellotto B.;Mazzari N.;
2024
Abstract
A conjecture recently stated by Flach and Morin relates the action of the monodromy on the Galois invariant part of the p-adic Beilinson–Hyodo–Kato cohomology of the generic fiber of a scheme defined over a DVR of mixed characteristic to (the cohomology of) its special fiber. We prove the conjecture in the case that the special fiber of the given arithmetic scheme is also a fiber of a geometric family over a curve in positive characteristic.
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