For a smooth proper hyperbolic curve over an algebraic closure of a p-adic local field and finitely many disjoint sufficiently small open disks, there is one connected finite étale cover with a component mapping isomorphically onto the entire disk exterior and every component above each disk having degree divisible by p.
For a smooth proper hyperbolic curve over an algebraic closure of a p-adic local field and finitely many disjoint sufficiently small open disks, there is one connected finite étale cover with a component mapping isomorphically onto the entire disk exterior and every component above each disk having degree divisible by p.
For a smooth proper hyperbolic curve over an algebraic closure of a p-adic local field and finitely many disjoint sufficiently small open disks, there is one connected finite étale cover with a component mapping isomorphically onto the entire disk exterior and every component above each disk having degree divisible by p.
If correct, gives a simultaneous covering construction useful in p-adic anabelian geometry beyond earlier one-point resolution-cover statements.
Can one finite étale cover preserve a chosen exterior sheet while forcing p-divisible degree above every prescribed disk?
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OpenAI reports an étale cover with prescribed exterior and disk degrees
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