Non-abelian Lefschetz hyperplane theorems
-- Daniel Litt, September 18, 2015

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How are the properties of a variety X related to those of an ample
divisor D in X?  Classical Lefschetz hyperplane theorems answer this
question by comparing the cohomology or homotopy type of X to that of
D.  I'll describe new results, encapsulating some of these older
Lefschetz theorems, which compare F(X) to F(D) where F is any functor
which is representable in a suitable sense.  While the main results
are in characteristic zero, the method of proof passes through
positive characteristic.