Towards a topological proof of Wright's Theorem

Malle's Conjecture concerns the asymptotic behavior of the number of degree-n extensions of a number field with Galois group permutation-isomorphic to G. Using the function field analogy, a similar conjecture can be made for finite extensions of F_q(t), where q is a power of a prime. In fact, a similar conjecture has been proven by Wright (1989), in the case where G is abelian. In this work, we also prove an asymptotic bound on the number of field extensions of F_q(t) in the abelian case, using substantially different methods. This serves to highlight connections between different fields within mathematics and to test the feasibility of the particular method outlined in this paper.

Author dc:creator

• de Langis, Mathieu

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/11299/270549

OAI identifier oai:identifier

oai:conservancy.umn.edu:11299/270549