Explicit Class Field Theory for global function fields

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Let F be a global function field and let F^ab be its maximal abelian extension. Following an approach of D.Hayes, we shall construct a continuous homomorphism \rho: Gal(F^ab/F) \to C_F, where C_F is the idele class group of F. Using class field theory, we shall show that our \rho is an isomorphism of topological groups whose inverse is the Artin map of F. As a consequence of the construction of \rho, we obtain an explicit description of F^ab. Fix a place \infty of F, and let A be the subring of F consisting of those elements which are regular away from \infty. We construct \rho by combining the Galois action on the torsion points of a suitable Drinfeld A-module with an associated \infty-adic representation studied by J.-K. Yu.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Explicit Class Field Theory for global function fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Explicit Class Field Theory for global function fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Explicit Class Field Theory for global function fields will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-319315

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.