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SUMMARY:Relative étale slices and cohomology of moduli spaces - Andrés I
 báñez Núñez (University of Oxford)
DTSTART:20240118T100000Z
DTEND:20240118T104500Z
UID:TALK209398@talks.cam.ac.uk
DESCRIPTION:We will explain a method to show that different moduli spaces 
 have the same topology or cohomology. This applies\, for example\, to modu
 li spaces of principal bundles on &nbsp\;two curves of the same genus or c
 ertain moduli spaces of sheaves on two different surfaces. The idea is to 
 consider families of moduli stacks and apply a new relative local structur
 e result to conclude that the associated family of good moduli spaces is &
 eacute\;tale locally trivial. From this\, the relevant cohomological prope
 rties 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.
LOCATION:Seminar Room 2\, Newton Institute
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