---
_id: '66312'
abstract:
- lang: eng
  text: Let $X$ be a complex abelian variety. We prove an analogue of both the (cohomological)
    $P=W$ conjecture and the geometric $P=W$ conjecture connecting the finer topological
    structure of the Dolbeault moduli space of topologically trivial semistable Higgs
    bundles on $X$ and the Betti moduli space of characters of the fundamental group
    of $X$. The geometric heart of our approach is the spectral data morphism for
    Dolbeault moduli spaces on abelian varieties that naturally factors the Hitchin
    morphism and whose target is not an affine space of pluricanonical sections, but
    a suitable symmetric product.
author:
- first_name: Barbara
  full_name: Bolognese, Barbara
  last_name: Bolognese
- first_name: Alex
  full_name: Küronya, Alex
  last_name: Küronya
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  ama: Bolognese B, Küronya A, Ulirsch M. $P=W$ phenomena on abelian varieties. <i>arXiv:230303734</i>.
    Published online 2023.
  apa: Bolognese, B., Küronya, A., &#38; Ulirsch, M. (2023). $P=W$ phenomena on abelian
    varieties. In <i>arXiv:2303.03734</i>.
  bibtex: '@article{Bolognese_Küronya_Ulirsch_2023, title={$P=W$ phenomena on abelian
    varieties}, journal={arXiv:2303.03734}, author={Bolognese, Barbara and Küronya,
    Alex and Ulirsch, Martin}, year={2023} }'
  chicago: Bolognese, Barbara, Alex Küronya, and Martin Ulirsch. “$P=W$ Phenomena
    on Abelian Varieties.” <i>ArXiv:2303.03734</i>, 2023.
  ieee: B. Bolognese, A. Küronya, and M. Ulirsch, “$P=W$ phenomena on abelian varieties,”
    <i>arXiv:2303.03734</i>. 2023.
  mla: Bolognese, Barbara, et al. “$P=W$ Phenomena on Abelian Varieties.” <i>ArXiv:2303.03734</i>,
    2023.
  short: B. Bolognese, A. Küronya, M. Ulirsch, ArXiv:2303.03734 (2023).
date_created: 2026-07-08T06:32:00Z
date_updated: 2026-07-08T06:32:25Z
external_id:
  arxiv:
  - '2303.03734'
language:
- iso: eng
publication: arXiv:2303.03734
status: public
title: $P=W$ phenomena on abelian varieties
type: preprint
user_id: '82981'
year: '2023'
...