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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.17358 |
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Table of Contents:
- We study $p$-adic manifolds associated with twisted points of quotient stacks $\mathcal{X} = [U/G]$ and their quotient spaces $π:\mathcal{X} \to X$. We prove several structural results about the fibres of $π$ and derive in particular a formula expressing $p$-adic integrals on $X$ in terms of the cyclotomic inertia stack of $\mathcal{X}$, generalizing the orbifold formula for Deligne-Mumford stacks. We then apply our formalism to moduli problems associated to hereditary abelian categories with symmetric Euler pairing, and show that their refined BPS-invariants are computed locally on the coarse moduli space by a $p$-adic integral. As a consequence we recover the $χ$-independence of these invariants for $1$-dimensional sheaves on del Pezzo surfaces previously proven by Maulik--Shen. Along the way we derive a new formula for the plethystic logarithm on the $λ$-ring of functions on $k$-linear stacks, which might be of independent interest.