University of British Columbia

Wed 25 Nov 2020, 2:00pm
Topology and related seminars
Zoom

Rational cuspidal curves, surfaces of BogomolovMiyaokaYau type, and rational homology cobordism: old and new problems at the crossroad of algebraic geometry and low dimensional topology.

Zoom
Wed 25 Nov 2020, 2:00pm3:00pm
Abstract
A classical problem in algebraic geometry asks what rational cuspidal curves can be realised in the complex projective plane. In the last few years some substantial advancement regarding this problem have been made, also based on the methods of Heegaard Floer homology. I will discuss some open problems, conjectures, and constructions. This is joint work with Paolo Aceto (Oxford University).
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University of Alberta

Wed 2 Dec 2020, 2:00pm
Topology and related seminars
Zoom

Motivic cohomology and infinitesimal group schemes

Zoom
Wed 2 Dec 2020, 2:00pm3:00am
Abstract
For k a perfect field of characteristic p > 0 and G a split reductive group over k with p a nontorsion prime for G, we compute the mod p motivic cohomology of the geometric classifying space BG_(r), where G_(r) is the rth Frobenius kernel of G. Our main tool is a motivic version of the EilenbergMoore spectral sequence, due to Krishna.
For a flat affine group scheme G/k of finite type, we define a cycle class map from the mod p motivic cohomology of the classifying space BG to the Hodge cohomology of the classifying stack BG. Assuming that G is split reductive with p a nontorsion prime for G and that the fundamental degrees of G are distinct, we show that this cycle map is injective for the Frobenius kernels G_(r).
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Seminar Information Pages

Note for Attendees
https://ubc.zoom.us/j/63532469289?pwd=b0RJYi9oOHAxRTY1QW5BOEdnMUU5Zz09