Abstract
In this note we prove the “quadratic property” of the boundary mapping in the exact sequence of cohomologies. We present calculations for the action of the Galois group on the Mumford group.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. Roquette, “On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras,” Math. Ann.,150, 411–439 (1962).
J. W. S. Cassels and A. Fröhlich, editors: Algebraic Number Theory, Thompson Book Co., Washington (1967).
D. Mumford, “On the equations defining abelian varieties, I,” Invent. Math.,1, 287–354 (1966).
M. I. Bashmakov, “Cohomologies of abelian varieties over a number field,” Usp. Matem. Nauk,27, No. 6, (168), 25–66 (1972).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 415–419, March, 1974.
In conclusion, the author thanks Yu. I. Manin for his statement of the problem and his interest in this paper; he also thanks V. G. Verkovich for useful discussions.
Rights and permissions
About this article
Cite this article
Zarkhin, Y.G. Noncommutative cohomologies and Mumford groups. Mathematical Notes of the Academy of Sciences of the USSR 15, 241–244 (1974). https://doi.org/10.1007/BF01438377
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01438377