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Non-commutative Jacobian conjecture via triangulated categories

Name
Alexander
Surname
Efimov
Scientific organization
National Research University Higher School of Economics
Academic degree
Scientific Researcher
Position
Scientific Researcher
Scientific discipline
Mathematics & Mechanics
Topic
Non-commutative Jacobian conjecture via triangulated categories
Abstract
The Jacobian conjecture states that any polynomial self-map of a complex affine space with constant nonzero Jacobian is an isomorphism.
I will recall the non-commutative version of this conjecture and explain how it can be proved via triangulated categories.
Keywords
Triangulated categories, localization, representation spaces
Summary

The main idea is to deduce the non-commutative Jacobian conjecture to a certain statement about localization of triangulated categories.