Syntomic cohomology and Beilinson’s Tate conjecture for 𝐾₂

Asakura, Masanori; Sato, Kanetomo

doi:10.1090/S1056-3911-2012-00591-8

Syntomic cohomology and Beilinson’s Tate conjecture for $K_2$

Authors: Masanori Asakura and Kanetomo Sato
Journal: J. Algebraic Geom. 22 (2013), 481-547
DOI: https://doi.org/10.1090/S1056-3911-2012-00591-8
Published electronically: October 3, 2012
MathSciNet review: 3048543
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Abstract | References | Additional Information

Abstract: We study Beilinson’s Tate conjecture for $K_2$ using the theory of syntomic cohomology. As an application, we construct integral indecomposable elements of $K_1$ of elliptic surfaces. Moreover, we give the first example of a surface $X$ with $p_g\ne 0$ over a $p$-adic field such that the torsion of $\mathrm {CH}_0(X)$ is finite.

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Additional Information

Masanori Asakura
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Email: asakura@math.sci.hokudai.ac.jp

Kanetomo Sato
Affiliation: Graduate school of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Address at time of publication: Department of Mathematics, Chuo University, Tokyo 112-8551, Japan
Email: kanetomo@math.nagoya-u.ac.jp, kanetomo_sato@hotmail.com

Received by editor(s): September 6, 2010
Received by editor(s) in revised form: March 23, 2011
Published electronically: October 3, 2012