English

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