# 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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