Parshin's conjecture expects that the higher algebraic $K$-groups of smooth projective varieties over a finite field are torsion. In this thesis we prove that with the assumption of finite generation of higher \'etale algebraic $K$-theory of smooth projective varieties over a finite field, one can reduce Parshin's conjecture to the case of surfaces. We use this technique to prove the Parshin's conjecture for symmetric power of smooth curves and Abelian varieties with the assumption of finite generation of \'etale $K$-theory.

Creator

• Yousefzadehfard, Aydin

DOI

• https://doi.org/10.21985/n2-mx2g-ww66

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15827
• etdadmin_upload_856824

Keyword

• Lefschetz
• Grothendieck
• Algebraic K-theory

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright