Crystalline Fundamental Groups II — Log Convergent Cohomology and Rigid Cohomology

By Atsushi Shiho. 2002

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Bounding Picard numbers of surfaces using p-adic cohomology (2006, methodology): “For the general construction, see for instance [43, Chapter 2].”
Finiteness of rigid cohomology with coefficients (2002, methodology): “. The gross outline of the proof follows that given by Berthelot [Be4] in the constant coeﬃcient case, that given by Tsuzuki [T2, Theorem 6.1.1] in the unit-root case, and the proposed proof of Shiho [S] in the general case. Proof of Theorem 1.1. We prove the following two assertions by induction on”
Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions (2004, background): “th proper varieties. With a semistable reduction theorem for overconvergent F-isocrystals, one hopes to obtain analogous results in rigid cohomology; we now describe some possible such results. Shiho [33] has shown that semistable reduction implies the ﬁnite dimensionality of rigid cohomology with c”