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arXiv · 1902.01882

Stability in the cohomology of the space of complex irreducible polynomials in several variables

Weiyan Chen
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Abstract

We 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 $d$ increases, and second, its compactly supported cohomology stabilizes as $n$ increases. Our topological results are inspired by counting results over finite fields due to Carlitz and Hyde.

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Weiyan Chen. 2019-09-05. Stability in the cohomology of the space of complex irreducible polynomials in several variables. https://doi.org/10.1093/imrn%2Frnz296

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