Geodesic
Local acyclicity in $p$-adic cohomology
Documenta mathematica, Tome 26 (2021), pp. 981-1044.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove an analogue for $p$-adic coefficients of the Deligne-Laumon theorem on local acyclicity for curves. That is, for an overconvergent $F$-isocrystal $E$ on a relative curve $f:U\rightarrow S$ admitting a good compactification, we show that the cohomology sheaves of $\mathbf{R}f_!E$ are overconvergent isocrystals if and only if $E$ has constant Swan conductor at infinity.
Classification : 14F30, 14G27, 14G22
Keywords: \(p\)-adic cohomology, Swan conductors, overconvergent \(F\)-isocrystals 
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     author = {Lazda, Christopher},
     title = {Local acyclicity in \(p\)-adic cohomology},
     journal = {Documenta mathematica},
     pages = {981--1044},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a30/}
}
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Lazda, Christopher. Local acyclicity in \(p\)-adic cohomology. Documenta mathematica, Tome 26 (2021), pp. 981-1044. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a30/