STNB2018 (32nd edition)
Algebraic Groups, Tannakian Categories and Applications
Presenters
Guillem Sala
Abstract
The theory of algebraic groups is the study of the properties of algebraic varieties that have been endowed with the structure of a group, defining multiplication, inversion and identity via regular maps. Once the notion of a representation from group theory to algebraic groups has been extended properly, the category of representations of an algebraic group G, denoted as Rep(G), can be constructed. In turn, this category can be given an extra structure to make it into a tannakian category. It is observed that tannakian formalism gives conditions so that algebraic groups can be recovered from its category of representations. Eventually, these results are applied to differential Galois theory.
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