The decomposition theorem for stacks of Higgs bundles


Event details

Date 02.12.2021 14:1516:00  
Speaker Ben Davison (Edinburgh Hodge Institute)
Category Conferences - Seminars
The BBDG decomposition theorem is a fundamental result on the cohomology of smooth varieties, which are proper over some base L, implying that the cohomology is filtered by the hypercohomology of perverse sheaves on the base L (I'll recall this part of the theory in the pre-talk).  
One of the most striking applications of this theory is to the topology of smooth moduli spaces of Higgs bundles, which admit a proper morphism, given by the Hitchin system.  Smoothness is arranged by fixing the rank and the degree of the Higgs bundles under consideration to be coprime.
In the main talk I will focus on what happens in the non-coprime case; the moduli space of Higgs bundles then becomes highly singular and stacky, so that the decomposition theorem doesn't (seem to) apply to the Hitchin system.  I'll explain why in fact the decomposition theorem still holds, and sketch an application to the famous P=W conjecture, connecting the perverse filtration defined via the decomposition theorem on the Dolbeault/Higgs side with the weight filtration on the Betti side of nonabelian Hodge theory.

Practical information

  • Informed public
  • Free


  • Dimitri Wyss


  • Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)

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