Drinfeld modules and subfields of division fields

Cristian Virdol

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1 Citation (Scopus)

Abstract

Let A = double-struck Fq[T], where double-struck Fq is a finite field, let Q = double-struck Fq(T), and let F be a finite extension of Q. Consider φ a Drinfeld A-module over F of rank r. We write r = hed, where E is the center of D :=End F{combining macron}(φ)⊗Q, e = [E : Q] and d = [D : E]1/2. For m ∈ A, let F (φ[m]) be the field obtained by adjoining to F the m-division points φ[m] of φ, and let F (φ[m])′ be the subfield of F (φ[m]) fixed by the scalar elements of Gal(F (φ[m])/F) ⊆ GLr(A/mA). In this paper, when r ≥ 3 and h ≥ 2, we study the splitting of the primes ℘ of F of degree x in the fields F (φ[m])′ and obtain an asymptotic formula which counts them.

Original languageEnglish
Pages (from-to)211-221
Number of pages11
JournalHouston Journal of Mathematics
Volume42
Issue number1
Publication statusPublished - 2016

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2015R1D1A1A01056643).

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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