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Relative étale slices and cohomology of moduli spaces

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EMG - New equivariant methods in algebraic and differential geometry

We will explain a method to show that different moduli spaces have the same topology or cohomology. This applies, for example, to moduli spaces of principal bundles on  two curves of the same genus or certain moduli spaces of sheaves on two different surfaces. The idea is to consider families of moduli stacks and apply a new relative local structure result to conclude that the associated family of good moduli spaces is étale locally trivial. From this, the relevant cohomological properties follow from vanishing cycles techniques. Over the complex numbers, we get homeomorphisms. This is joint work with Mark Andrea de Cataldo and Andres Fernandez Herrero.

This talk is part of the Isaac Newton Institute Seminar Series series.

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