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Title:
Artin’s theorems in supergeometry
Speaker:
Abstract:
Artin’s theorems on approximation and algebraization of formal deformations and stacks give general criteria for functors to be, in various senses, described by algebraic objects. It has long been expected that analogous results hold in supergeometry, however proofs of the full suite of Artin theorems have remained absent from the supergeometry literature. One reason for this may be the sense that establishing the Artin theorems in supergeometry would require the tedious repetition of various difficult arguments in commutative algebra, deformation theory, and algebraic geometry. I have recently proved the Artin theorems in the super case. Moreover, at several key points I was able to reduce to the (known) bosonic case by an argument which is significantly simpler than the original bosonic argument. In my talk I will show how to use the Artin theorem to construct some moduli spaces of interest in supergeometry, e.g.,the Picard (super)stack.
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