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Big mod [l] monodromy for families of [G] covers

Author / Creator
Jain, Lalit Kumar, author
Available as
Online
Physical
Summary

The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, ar...

The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to the monodromy of specific families. In general, we expect the monodromy of a family to be "big'', i.e. as large as possible subject to any geometrical or algebraic constraints arising from the family. In this thesis I study the monodromy of Hurwitz spaces of [G]-covers, moduli spaces for branched covers of the projective line with Galois group [G]. I show that if [G] is center-free and has trivial Schur multiplier the mod [l] monodromy will be big as long as the number of branch points of a curve in the family is chosen to be sufficiently large. Along the way the necessary algebraic results, including a generalized equivariant Witt's lemma, are presented. The proof relies on a characterization of the connected components of Hurwitz Spaces due to Ellenberg, Venkatesh, and Westerland that generalizes an older result of Conway-Parker and Fried Völklein. Connections to current results on monodromy of cyclic covers are also discussed.

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Creator
by Lalit Jain
Format
Books
Publication
  • 2016
Physical Details
  • vi, 63 leaves : illustrations ; 29 cm
OCLC
ocn956736166, ocn968332337

  • On title page [l] is represented by a script "l".
  • On title page [G] is italicized.
  • Adviser: Jordan S. Ellenberg.
  • Ph.D. University of Wisconsin--Madison 2016.
  • Print reproduction.
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