Motivic cohomology and \(K\)-theory of some surfaces over finite fields

DOI10.1016/j.jpaa.2023.107518arXiv2302.09867OpenAlexW4386101782MaRDI QIDQ6185293

Oliver Gregory

Publication date: 8 January 2024

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.09867

Mathematics Subject Classification ID

(K)-theory of schemes (19E08) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15)

Cites Work

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• The Tate conjecture for \(K3\) surfaces over finite fields
• The Tate conjecture for \(K3\) surfaces in odd characteristic
• Weil-étale cohomology over finite fields
• The period-index problem in WC-groups. IV: A local transition theorem
• Application d'Abel-Jacobi p-adique et cycles algébriques. (p-adic Abel- Jacobi map and algebraic cycles)
• Groupes de Chow et K-théorie de variétés sur un corps fini
• Torsion dans le groupe de Chow de codimension deux
• Motifs, L-functions, and the K-cohomology of rational surfaces over finite fields
• Algebraic cycles and higher K-theory
• On the cycle map for torsion algebraic cycles of codimension two
• Enriques' classification of surfaces in char p. III
• Some results on unirationality of algebraic surfaces
• On values of zeta functions and \(\ell\)-adic Euler characteristics
• Applications of weight-two motivic cohomology
• Bott elements in algebraic \(K\)-theory
• Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\)
• An example of unirational surfaces in characteristic \(p\)
• The \(K\)-theory of fields in characteristic \(p\)
• A variational Tate conjecture in crystalline cohomology
• Some consequences of the Riemann hypothesis for varieties over finite fields
• Unramified class field theory of arithmetical surfaces
• Motives of isogenous \(K3\) surfaces
• Supersingular \(K3\) surfaces are unirational
• Remarks on motives of abelian type
• Endomorphisms of Abelian varieties over finite fields
• On the cohomology and K-theory of the general linear groups over a finite field
• Remarks on Correspondences and Algebraic Cycles
• Lectures on K3 Surfaces
• Algebraic $K$-theory and etale cohomology
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• Supersingular $K3$ surfaces
• Formal groups arising from algebraic varieties
• Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
• The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky
• First and second K-groups of an elliptic curve over a global field of positive characteristic
• Cycles, derived categories, and rationality
• The Weil-étale topology on schemes over finite fields
• Invariants of Fano varieties in families