The Galois action on symplectic K-theory
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The Galois action on symplectic K-theory. / Feng, Tony; Galatius, Soren; Venkatesh, Akshay.
In: Inventiones Mathematicae, Vol. 230, 2022, p. 225-319.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Galois action on symplectic K-theory
AU - Feng, Tony
AU - Galatius, Soren
AU - Venkatesh, Akshay
N1 - Publisher Copyright: © 2022, The Author(s).
PY - 2022
Y1 - 2022
N2 - We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Zp(2 k- 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.
AB - We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Zp(2 k- 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.
U2 - 10.1007/s00222-022-01127-8
DO - 10.1007/s00222-022-01127-8
M3 - Journal article
AN - SCOPUS:85133598266
VL - 230
SP - 225
EP - 319
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
ER -
ID: 344720611