Varieties over ℚ with infinite Chow groups modulo almost all primes

2023/07/11 by Federico Scavia, Scavia, Federico
Mathematics · #14C15 (Primary) 14C25 #14K05 #14K22 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2307.05729

openalex publication_date 2023/07/11 · openalex created_date 2023/07/14 · openalex updated_date 2026/07/28

Abstract

Let E be the Fermat cubic curve over ℚ. In 2002, Schoen proved that the group CH²(E³)/ℓ is infinite for all primes ℓ≡ 1\pmod 3. We show that CH²(E³)/ℓ is infinite for all prime numbers ℓ> 5. This gives the first example of a smooth projective variety X over ℚ such that CH²(X)/ℓ is infinite for all but at most finitely many primes ℓ. A key tool is a recent theorem of Farb--Kisin--Wolfson, whose proof uses the prismatic cohomology of Bhatt--Scholze.

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• Intermediate modular curves with infinitely many cubic points over ℚ
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