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

被引：0

作者：

Gregory, Oliver ^{[1
,2
]}

机构：

[1] Imperial Coll London, Huxley Bldg, London SW7 2AZ, England

[2] Heilbronn Inst Math Res, Bristol, Avon, England

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2024年 / 228卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

ALGEBRAIC CYCLES; VARIETIES; CONJECTURE; TORSION;

D O I：

10.1016/j.jpaa.2023.107518

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute the algebraic K-theory of some classes of surfaces defined over finite fields. We achieve this by first calculating the motivic cohomology groups and then studying the motivic Atiyah-Hirzebruch spectral sequence. In an appendix, we slightly enlarge the class of surfaces for which Parshin's conjecture is known.Crown Copyright & COPY; 2023 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

引用

页数：21

共 47 条

[1] [Anonymous], 1996, Doc. Math.
[2] ARTIN M, 1977, ANN SCI ECOLE NORM S, V10, P87
[3] ARTIN M, 1974, ANN SCI ECOLE NORM S, V7, P543
[4] Cycles, derived categories, and rationality
Auel, Asher
Bernardara, Marcello
[J]. SURVEYS ON RECENT DEVELOPMENTS IN ALGEBRAIC GEOMETRY, 2017, 95 : 199 - 266
[5] VALUES OF ZETA FUNCTIONS AND L-ADIC EULER CHARACTERISTICS
BAYER, P
NEUKIRCH, J
[J]. INVENTIONES MATHEMATICAE, 1978, 50 (01) : 35 - 64
[6] REMARKS ON CORRESPONDENCES AND ALGEBRAIC CYCLES
BLOCH, S
SRINIVAS, V
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1983, 105 (05) : 1235 - 1253
[7] ALGEBRAIC CYCLES AND HIGHER K-THEORY
BLOCH, S
[J]. ADVANCES IN MATHEMATICS, 1986, 61 (03) : 267 - 304
[8] ENRIQUES CLASSIFICATION OF SURFACES IN CHAR-P .3.
BOMBIERI, E
MUMFORD, D
[J]. INVENTIONES MATHEMATICAE, 1976, 35 : 197 - 232
[9] Bragg D, 2019, Arxiv, DOI arXiv:1804.07282
[10] The Tate conjecture for K3 surfaces over finite fields
Charles, Francois
[J]. INVENTIONES MATHEMATICAE, 2013, 194 (01) : 119 - 145

← 1 2 3 4 5 →