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Nov 10, 2019 at 0:21 comment added Daniel Litt You may enjoy: arxiv.org/abs/0902.3464
Nov 10, 2019 at 0:21 comment added LSpice @anon's link, clickably: Milne - The work of John Tate.
Nov 9, 2019 at 23:01 history edited Kim CC BY-SA 4.0
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Nov 9, 2019 at 22:35 comment added Kim So there is no general construction yet for a smooth projective scheme over $\mathbf{Q}_q$? Is there any consensus on whether such a thing should exist?
Nov 9, 2019 at 13:40 comment added anon Sixty years ago Tate showed the answer is yes for an elliptic curve over $\mathbb{Q}_p$ whose reduction mod p has a node with tangents rational over the base field. Since then there has been a huge amount of work. For a brief friendly introduction, see Section 3 of Milne's article "The Work of John Tate", available on his webpage jmilne.org/math/ under Expository Notes.
Nov 8, 2019 at 1:27 comment added user145520 something like Tate uniformization is potentially relevant.
Nov 8, 2019 at 0:13 history edited Kim CC BY-SA 4.0
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Nov 8, 2019 at 0:07 history asked Kim CC BY-SA 4.0