Does the Grothendieck ring of varieties contain nilpotent elements?

2025/08/15 by Anna Bot, Bot, Anna, Alessio Cangini +3
Computer Science · Mathematics · #14A10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.10464

openalex publication_date 2025/08/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We show that a ring closely related to the Grothendieck ring of varieties has nilpotent elements, provided that the characteristic of the ground field is equal to 11 or at least 17.

Citations

• On the Grothendieck ring of varieties in positive characteristic
• The universal Euler characteristic for varieties of characteristic zero

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• Global coefficient ring in the nilpotence conjecture
• The coefficient field in the nilpotence conjecture for toric varieties
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