A Neron-Ogg-Shafarevich criterion for $K3$ surfaces

Abstract: The naive analogue of the Néron-Ogg-Shafarevich criterion fails for $K3$ surfaces, that is, there exist $K3$ surfaces over Henselian, discretely valued fields $\mathbb{K}$, with unramified étale cohomology groups, but which do not admit good reduction over $\mathbb{K}$. Assuming potential semi-stable reduction, I will show how to correct this by proving that a $K3$ surface has good reduction if and only if is second cohomology is unramified, and the associated Galois representation over the residue field coincides with the second cohomology of a certain "canonical reduction" of $X$. This is joint work with B. Chiarellotto and C. Liedtke.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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