Degenerations and limit Frobenius structures in rigid cohomology
Number Theory
2019-02-20 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0912.5185,
title = {Degenerations and limit Frobenius structures in rigid cohomology},
author = {Alan G. B. Lauder},
journal= {arXiv preprint arXiv:0912.5185},
year = {2019}
}
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41 pages