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Jun 2, 2018 at 10:51 vote accept Y. M.
May 28, 2018 at 22:37 answer added Avi Steiner timeline score: 3
May 27, 2018 at 19:54 comment added Will Sawin I'm not a $D$-module expert but I'm pretty sure the answer is no. If you take a $D$-module $M$ supported on the special fiber you should get the simple module supported at $p$ tensored with the cohomology of $M$, and already for $X$ a smooth surface, so the exceptional divisor is $\mathbb P^1$, the cohomology can be arbitrarily large.
May 27, 2018 at 13:00 history edited Y. M. CC BY-SA 4.0
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May 27, 2018 at 12:51 history edited Y. M. CC BY-SA 4.0
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May 27, 2018 at 12:42 history asked Y. M. CC BY-SA 4.0