MARC Bibliographic Record

LEADER02615nam a2200385Ki 4500
001 991022121425802122
005 20171120073337.0
006 m o d s
007 cr mn|||||||||
008 160816s2016 wiua obm 000 0 eng d
024 7_ $a1711.dl/XRLTIOFBXLSHB8U$2hdl
035    $a(OCoLC)ocn956736166
035    $a(EXLNZ-01UWI_NETWORK)9912229759002121
040    $aGZM$beng$erda$cGZM
049    $aGZMA
100 1_ $aJain, Lalit Kumar,$edissertant.
245 10 $aBig mod [l] monodromy for families of [G] covers /$cby Lalit Jain.
264 _1 $a[Madison, Wis.] :$b[University of Wisconsin--Madison],$c2016.
300    $a1 online resource (vi, 63 pages) :$billustrations
336    $atext$btxt$2rdacontent
337    $acomputer$bc$2rdamedia
338    $aonline resource$bcr$2rdacarrier
500    $aOn title page [l] is represented by a script "l".
500    $aOn title page [G] is italicized.
500    $aAdviser: Jordan S. Ellenberg.
520    $aThe 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.
502    $bPh.D.$cUniversity of Wisconsin--Madison$d2016.
504    $aIncludes bibliographical references (pages 59-63).
588    $aDescription based on online resource; title from title page (viewed August 1, 2016).
653    $aMathematics.
653    $aAlgebraic Geometry.
653    $aMonodromy.
653    $aNumber Theory.
690    $aDissertations, Academic$xMathematics.$9local
856 40 $uhttp://digital.library.wisc.edu/1711.dl/5ACJP2ZOUB75Q8L
950    $a20160816$bjlm$co$de$egls$9local

MMS IDs

Document ID: 9912229759002121
Network Electronic IDs: 9912229759002121
Network Physical IDs:
mms_mad_ids: 991022121425802122