Website Search
Find information on spaces, staff, and services.
Find information on spaces, staff, and services.
| LEADER | 02489nam a2200373Ki 4500 | |
| 001 | 991022160510702122 | |
| 005 | 20180324202404.0 | |
| 008 | 170113s2016 wiua rm 000 0 eng d | |
| 024 | 8_ | $aUMI 10142669 |
| 035 | $a(OCoLC)968332337 | |
| 035 | $a(OCoLC)ocn968332337 | |
| 035 | $a(EXLNZ-01UWI_NETWORK)9912282868002121 | |
| 040 | $aGZM$beng$erda$epn$cGZM | |
| 049 | $aGZMA | |
| 100 | 1_ | $aJain, Lalit Kumar,$eauthor. |
| 245 | 10 | $aBig mod [l] monodromy for families of [G] covers /$cby Lalit Jain. |
| 264 | _0 | $c2016. |
| 300 | $avi, 63 leaves :$billustrations ;$c29 cm | |
| 336 | $atext$btxt$2rdacontent | |
| 337 | $aunmediated$bn$2rdamedia | |
| 338 | $avolume$bnc$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. | |
| 533 | $aPrint reproduction. | |
| 653 | $aMathematics. | |
| 653 | $aAlgebraic Geometry. | |
| 653 | $aMonodromy. | |
| 653 | $aNumber Theory. | |
| 690 | $aDissertations, Academic$xMathematics.$9local | |
| 776 | 08 | $iOnline version:$aJain, Lalit Kumar.$tBig mod [l] monodromy for families of [G] covers.$w(OCoLC)956736166 |
| 856 | 41 | $uhttp://digital.library.wisc.edu/1711.dl/5ACJP2ZOUB75Q8L |
| 950 | $a20170113$blmb$co$de$egls$9local | |
| LEADER | 02615nam 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 | |