- Award ID(s):
- 1855536
- NSF-PAR ID:
- 10172347
- Date Published:
- Journal Name:
- Séminaire lotharingien de combinatoire
- Issue:
- 82B
- ISSN:
- 1286-4889
- Page Range / eLocation ID:
- #57
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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 the essential $p$ -dimension of congruence covers of the moduli space of genus $g$ curves, as well as its hyperelliptic locus, and of certain locally symmetric varieties. These results include cases where the locally symmetric variety $M$ is proper . As far as we know, these are the first examples of nontrivial lower bounds on the essential dimension of an unramified, nonabelian covering of a proper algebraic variety.more » « less
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This is the first of our papers on quasi-split affine quantum symmetric pairs
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In this paper we study some classical complexity-theoretic questions regarding G
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GI . Unlike the graph coloring gadgets, which support restricting to various subgroups of the symmetric group, the problems we study require restricting to various subgroups of the general linear group, which entails significantly different and more complicated gadgets.The analysis of one of our gadgets relies on a classical result from group theory regarding random generation of classical groups (Kantor & Lubotzky, Geom. Dedicata, 1990). For the nilpotency class reduction, we combine a runtime analysis
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Abstract It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.
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