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Frobenius lifts and correspondences on GL_n

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Alexandru Buium
University of New Mexico/MPIM
Mit, 2019-07-03 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Let GL_n be the general linear group scheme over the integers.We show that the p-adic completion of GL_n possessescertain remarkable Frobenius lifts attached to integral symmetric matrices; these Frobenius liftscan be viewed as  arithmetic analogues, for Spec Z,  of the Levi-Civita connection attached to a metric on a manifold. We then show how these Frobeniuslifts admit algebraizations by correspondences on GL_n; the commutatorsof these correspondences can be viewed as an arithmetic analogue, for Spec Z, of Riemannian curvature. 

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