Abstract
AbstractWe prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d\to \infty $, and second, its compactly supported cohomology stabilizes as $n\to \infty $. Our topological results are inspired by counting results over finite fields due to Carlitz and Hyde.
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