2019/05/25 by Piotr Krasoń, Krasoń, Piotr
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1905.10637
openalex publication_date 2019/05/25 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this paper we investigate a local to global principle for Galois\ncohomology of number fields with coefficients in the Tate module of an abelian\nvariety. In citebk13 G. Banaszak and the author obtained the sufficient\ncondition for the validity of the local to global principle for 'etale\nK-theory of a curve . This condition in fact has been established by means of\nan analysis of the corresponding problem in the Galois cohomology. We show that\nin some cases this result is the best possible i.e if this condition does not\nhold we obtain counterexamples.\n We also give some examples of curves and their Jacobians. Finally, we prove\nthe dynamical version of the local to global principle for 'etale K-theory\nof a curve. The dynamical local to global principle for the groups of\nMordell-Weil type has recently been considered by S. Bara 'nczuk in\n citeb17. We show that all our results remain valid for Quillen K-theory of\n cal X if the Bass and Quillen-Lichtenbaum conjectures hold true for cal\nX.\n