Abstract
If X is a smooth, projective variety over a number field k, then the absolute Galois group Gk = Gal(k̄/k) acts on the étale cohomology groups Hi(X̄, ℚℓ/ℤℓ(n)), where X̄ = X Xk k̄ for an algebraic closure k̄ of k. In this paper I study some properties of these Gk-modules; in particular, I am interested in the corank of the Galois cohomology groups $${H^v}\,({G_k},{H^i}(\bar X,\,{Q_\ell }/{Z_\ell }(n))).$$ KeywordsExact SequenceAbelian VarietyChern ClassNumber FieldGood ReductionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
