Degenerations and limit Frobenius structures in rigid cohomology

Details Degenerations and limit Frobenius structures in rigid cohomology Degenerations and limit Frobenius structures in rigid cohomology

2009-12-28

arxiv.org/abs/0912.5185v1

Mathematics

Number Theory

41 pages

Scientific paper

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be effectively computable in an appropriate sense for a degeneration of projective hypersurfaces. We conjecture that the limiting Frobenius structure relates to the rigid cohomology of a semistable limit of the degeneration through an analogue of the Clemens-Schmidt exact sequence. Our construction is illustrated, and conjecture supported, by a selection of explicit examples.

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