Proof of the Parshin's Conjecture

2020/11/11 by Aydin Yousefzadehfard, Yousefzadehfard, Aydin
Computer Science · Mathematics · #19D99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Coding theory and cryptography #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2011.05544

openalex publication_date 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the Parshin's conjecture on the rational triviality of the higher algebraic K-theory of smooth projective varieties over finite fields. This is known to imply the Beilinson-Soulé conjecture for the fields of positive characteristic. Especially it implies that for a field F of char p and n>0, the only rationally non-trivial weight appearing in K_n(F)⊗ ℚ can be n, thus K_n(F)⊗ ℚ=K_n^M(F)⊗ ℚ where K_n^M(F) is the Milnor K-theory.

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