|Speaker :||Dhyan Aranha (Universitat Duisburg-Essen)|
|Title :||The Intrinsic Normal for Artin Stacks|
|Time :||2021-12-09 (Thu) 16:00 - 17:00|
|Place :||Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)|
We will report on joint work with Piotr Pstragowski where we extend the construction of the normal cone of a closed embedding of schemes to any locally of finite type morphism of higher Artin stacks and show that in the Deligne-Mumford case our construction recovers the relative intrinsic normal cone of Behrend and Fantechi. In this work we are able to characterize our extension as the unique one satisfying a short list of axioms, and use it to construct the deformation to the normal cone. As an application of our methods to any relative perfect obstruction theory on Artin stacks we can associate a virtual fundamental class.