Abstract Consider the algebraic function $\Phi _{g,n}$ that assigns to a general $g$ dimensional abelian variety an $n$ torsion point. A question first posed by Klein asks: What is the minimal $d$ such that, after a rational change of variables, the function $\Phi _{g,n}$ can be written as an algebraic function of $d$ variables? Using techniques from the deformation theory of $p$ divisible groups and finite flat group schemes, we answer this question by computing the essential dimension and $p$ dimension of congruence covers of the moduli space of principally polarized abelian varieties. We apply this result to compute themore »
Factorization problems in complex reflection groups
We enumerate factorizations of a Coxeter element into arbitrary factors in
the complex reflection groups G(d, 1, n) (the wreath product of the symmetric group
with a cyclic group) and its subgroup G(d, d, n), applying combinatorial and algebraic
methods, respectively. After a change of basis, the coefficients that appear are the same
as those that appear in the corresponding enumeration in the symmetric group.
 Award ID(s):
 1855536
 Publication Date:
 NSFPAR ID:
 10172347
 Journal Name:
 Séminaire lotharingien de combinatoire
 Issue:
 82B
 Page Range or eLocationID:
 #57
 ISSN:
 12864889
 Sponsoring Org:
 National Science Foundation
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