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arXiv · 2512.15575

Group actions on $p$-adic symplectic manifolds

Luis Crespo·Álvaro Pelayo
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Abstract

Let $p$ be a prime number. We introduce symplectic actions of $p$-adic analytic Lie groups on $p$-adic symplectic manifolds. Then we show that any $p$-adic symplectic action $G\times(M,\omega)\to(M,\omega)$ has a momentum map $\mu:M\to\mathfrak{g}^*$, and that a proper $p$-adic symplectic action is Hamiltonian if and only if every orbit is isotropic. We conclude by defining $p$-adic symplectic toric manifolds, by analogy with the real case.

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Luis Crespo, Álvaro Pelayo. 2025-12-17. Group actions on $p$-adic symplectic manifolds. https://arxiv.org/abs/2512.15575

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