MSI Colloquium

4pm Thursday 26 August 2004
James Borger
University of Chicago

Witt vectors and real mathematics

In the 1930s, around the time homology theory for manifolds was maturing, Witt introduced a bizarre algebraic construction that has come to be known as the ring of Witt vectors. The Witt vectors remained something of a curiosity until the 1970s, when they were put to work in the also maturing (by then) theory of cohomology for spaces of arithmetic interest, namely in studying the p-adic analogues of de Rham cohomology and Hodge theory. While their otherworldliness may have since faded, it is only because of this exposure to the sun, not because of an increase in our understanding.

In this talk, I will explain what the Witt vectors are and say something about how they have been used in arithmetic cohomology theories, and I'll conclude by discussing a new, natural chapter of algebra in which Witt's construction finally finds a home.




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