Tilman Bauer: p-Polar Rings
Time: Wed 2021-06-16 13.15 - 14.15
Location: Zoom, meeting ID: 685 0671 8075
Lecturer: Tilman Bauer (KTH)
Abstract: For a prime p, a p-polar ring is a graded abelian group with a p-fold multiplication map, defined on p-tuples of homogeneous elements of equal degree, satisfying suitable associativity and commutativity conditions. Commutative, nonunital (graded) rings are examples of p-polar rings, but they are far from the only ones. In this talk, I will focus on p-polar k-algebras over a perfect field k of characteristic p. A common theme of the results I will present is that commutative affine (p-adic) group schemes are naturally group objects not on the category of affine schemes but on the category of p-polar affine schemes, i.e. the opposite category of p-polar k-algebras. I will make use of p-typical Witt vectors, the technical heart of my results being that they are in fact well-defined for p-polar rings.
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