BPS invariants from p-adic integrals

Article Article scientifique Article BPS invariants from p-adic integrals eng 2024-05-30 2024-07 author Carocci Francesca 0000-0002-2601-0501 416819 author Orecchia Giulio author Wyss Dimitri 1525-1550 10.1112/s0010437x24007176 0010-437X https://www.cambridge.org/core/product/identifier/S0010437X24007176/type/journal_article We define $p$ -adic $\mathrm {BPS}$ or $p\mathrm {BPS}$ invariants for moduli spaces $\operatorname {M}_{\beta,\chi }$ 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 $\mu _{\rm can}$ on the $F$ -analytic manifold associated to $\operatorname {M}_{\beta,\chi }$ and the $p\mathrm {BPS}$ invariants are integrals of natural ${\mathbb {G}}_m$ gerbes with respect to $\mu _{\rm can}$ . A similar construction can be done for meromorphic and usual Higgs bundles on a curve. Our main theorem is a $\chi$ -independence result for these $p\mathrm {BPS}$ invariants. For one-dimensional sheaves on del Pezzo surfaces and meromorphic Higgs bundles, we obtain as a corollary the agreement of $p\mathrm {BPS}$ with usual $\mathrm {BPS}$ invariants through a result of Maulik and Shen [ Cohomological $\chi$ -independence for moduli of one-dimensional sheaves and moduli of Higgs bundles , Geom. Topol. 27 (2023), 1539–1586]. Dewey 510 25 Section de mathématiques 11 false Compositio mathematica 160 7 b9900ef4-484a-49b1-9d8e-c28e2b0778c3 Article (Published version) Restricted Article_scientifique_from_crossref.pdf 659030 application/pdf 1f5c0c431004af04a9531c149fff06290bc964321ba3a4a7c0d245219ceb79a6 restrictedAccess Faculté des sciences / Section de mathématiques

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BPS invariants from p-adic integrals	Compositio mathematica			2024	2	0

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Carocci, Francesca