2022/10/26 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2210.14866
openalex publication_date 2022/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that in either the convergent or overconvergent setting, an absolutely irreducible F-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic p, further equipped with actions of the partial Frobenius maps, is an external product of F-isocrystals over the multiplicands. The corresponding statement for lisse ℚ_ℓ-sheaves, for ℓ ≠ p a prime, is a consequence of Drinfeld's lemma on the fundamental groups of absolute products of schemes in characteristic p. The latter plays a key role in V. Lafforgue's approach to the Langlands correspondence for reductive groups with ℓ-adic coefficients; the p-adic analogue will be considered in subsequent work with Daxin Xu.