Topology of mathbbGₘ-actions and applications to the moduli of Higgs bundles

Key Points

• The aim is to explore the topology of varieties and stacks with $_m$ actions and apply these findings to Higgs bundles.
• Investigated the actions of the multiplicative group $_m$ on various varieties and stacks.
• Applied cohomological techniques to establish isomorphisms of cohomology rings.
• Focused on upgrading the Nonabelian Hodge Theorem in positive characteristic.
• Achieved a cohomological isomorphism of the cohomology rings compatible with cup product.
• Demonstrated the application of these techniques to the moduli of Higgs bundles.
• Provided new insights into the interactions between topology and algebraic structures under $_m$ actions.