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- W2963897584 abstract "In this paper we prove a semistable version of the variational Tate conjecture for divisors in crystalline cohomology, showing that for $k$ a perfect field of characteristic $p$ , a rational (logarithmic) line bundle on the special fibre of a semistable scheme over $kunicode[STIX]{x27E6}tunicode[STIX]{x27E7}$ lifts to the total space if and only if its first Chern class does. The proof is elementary, using standard properties of the logarithmic de Rham–Witt complex. As a corollary, we deduce similar algebraicity lifting results for cohomology classes on varieties over global function fields. Finally, we give a counter-example to show that the variational Tate conjecture for divisors cannot hold with $mathbb{Q}_{p}$ -coefficients." @default.
- W2963897584 created "2019-07-30" @default.
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- W2963897584 date "2019-05-01" @default.
- W2963897584 modified "2023-10-14" @default.
- W2963897584 title "Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz theorem" @default.
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- W2963897584 doi "https://doi.org/10.1112/s0010437x19007164" @default.
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