Algebraic K-theory and sums-of-squares formulas, by Daniel Dugger and Daniel C. Isaksen

We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to produce obstruction conditions when the field is the real numbers. Our result applies to arbitrary fields not of characteristic 2, making use of algebraic K-theory in place of topological K-theory.

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