Institut für Mathematik


Modul:   MAT770  Oberseminar: Algebraische Geometrie

Localization theorem for algebraic stacks

Vortrag von Dr. Charanya Ravi

Sprecher eingeladen von: Prof. Dr. Joseph Ayoub

Datum: 23.05.22  Zeit: 13.15 - 14.45  Raum:

The classical Atiyah-Bott localization theorem gives an isomorphism between the equivariant cohomology of a space X with action of a torus T with the cohomology of its fixed locus after inverting finitely many elements in the cohomology of BT. Further when X is smooth, there is an explicit formula for classes in the equivariant cohomology of X in terms of classes in the ordinary cohomology of the fixed locus and the normal bundle of the fixed locus. This theorem finds applications in enumerative geometry when the parameter space has a natural torus action. The need to access more general parameter spaces in algebraic-geometric setting (singular and stacky) and the need for refined counts (in other cohomology theories) motivates the need for a more general localization theorem and localization formula. In this talk, based on a joint work in progress with Dhyan Aranha, Adeel Khan, Alexei Latyntsev and Hyeonjun Park, we will discuss such a unified Atiyah-Bott localization theorem for equivariant cohomology theories of possibly singular algebraic stacks with an action of a linear algebraic group.

Topic: UZH Algebraic Geometry Seminar
Time: May 23, 2022 01:00 PM Zurich

Meeting ID: 625 5706 5336
Passcode: agseminar

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