On the connectedness of $p$-adic period domains

Ian Gleason; Jo\~ao Louren\c{c}o

On the connectedness of $p$-adic period domains

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arxiv 2210.08625 v2 pith:YKAMYCQ6 submitted 2022-10-16 math.NT math.AG

Ian Gleason , João Lourenço This is my paper · ORCID

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keywords adicdomainsperiodshimuraanaloguesanswersconnectedconnectedness

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abstract

We prove that all $p$-adic period domains (and their non-minuscule analogues) are geometrically connected. This answers a question of Hartl [Har13] and has interesting consequences to the geometry of Shimura and local Shimura varieties.

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Towards a p-adic nowhere density conjecture of Hecke Orbits
math.NT 2025-06 conditional novelty 6.0 of 10

A formal density theorem says that, under a Newton-Hodge irreducibility condition, deformations of a mod p point with large p-adic monodromy are open dense in every p-adic neighborhood.

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