BPS invariants from p-adic integrals

We define p-adic BPS or pBPS invariants for moduli spaces Mβ,χ of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure μcan on the F-analytic man ifold associated to Mβ,χ and the pBPS invariants are integrals of natural Gm gerbes with respect to μcan. A similar construction can be done for meromorphic and usual Higgs bundles on a curve. Our main theorem is a χ-independence result for these pBPS invariants. For one-dimensional sheaves on del Pezzo surfaces and meromor phic Higgs bundles, we obtain as a corollary the agreement of pBPS with usual BPS invariants through a result of Maulik and Shen [Cohomological χ-independence for mod uli of one-dimensional sheaves and moduli of Higgs bundles,Geom.Topol.27 (2023), 1539–1586].