- Title
- Explicit Drinfeld moduli schemes and Abhyankar’s generalized iteration conjecture
- Creator
- Breuer, Florian
- Relation
- Journal of Number Theory Vol. 160, p. 432-450
- Publisher Link
- http://dx.doi.org/10.1016/j.jnt.2015.08.021
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2016
- Description
- Let k be a field containing Fq. Let ψ be a rank r Drinfeld Fq[t]-module determined by ψt(X) = tX + a₁Xq+···+ar−1Xqr−1+Xqr, where t, a₁,...,ar−1 are algebraically independent over k. Let n ∈ Fq[t] be a monic polynomial. We show that the Galois group of ψₙ(X) over k(t, a₁,...,ar−1) is isomorphic to GLr(Fq[t]/nFq[t]), settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level tn. Video. For a video summary of this paper, please visit https://youtu.be/TInrNq02-UA.
- Subject
- Drinfeld modules; Drinfeld moduli schemes; Galois groups
- Identifier
- http://hdl.handle.net/1959.13/1437152
- Identifier
- uon:40248
- Identifier
- ISSN:0022-314X
- Language
- eng
- Reviewed
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