000 04008nam a22004935i 4500
001 978-0-387-23534-9
003 DE-He213
005 20161121230923.0
007 cr nn 008mamaa
008 100301s2005 xxu| s |||| 0|eng d
020 _a9780387235349
_9978-0-387-23534-9
024 7 _a10.1007/b101762
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
245 1 0 _aProgress in Galois Theory
_h[electronic resource] :
_bProceedings of John Thompson’s 70th Birthday Conference /
_cedited by Helmut Voelklein, Tanush Shaska.
264 1 _aBoston, MA :
_bSpringer US,
_c2005.
300 _aX, 168 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v12
505 0 _aSupplementary Thoughts on Symplectic Groups -- Automorphisms of the Modular Curve -- Reducing the Fontaine-Mazur Conjecture to Group Theory -- Relating Two Genus 0 Problems of John Thompson -- Relatively Projective Groups as Absolute Galois Groups -- Invariants of Binary Forms -- Some Classical Views on the Parameters of the Grothendieck-Teichmüller Group -- The Image of a Hurwitz Space Under the Moduli Map -- Very Simple Representations: Variations on a Theme of Clifford.
520 _aA recent trend in the field of Galois theory is to tie the previous theory of curve coverings (mostly of the Riemann sphere) and Hurwitz spaces (moduli spaces for such covers) with the theory of algebraic curves and their moduli spaces. A general survey of this is given in the article by Voelklein. Further exemplifications come in the articles of Guralnick on automorphisms of modular curves in positive characteristic, of Zarhin on the Galois module structure of the 2-division points of hyperelliptic curves and of Krishnamoorthy, Shashka and Voelklein on invariants of genus 2 curves. Abhyankar continues his work on explicit classes of polynomials in characteristic p>0 whose Glaois groups comprise entire families of Lie type groups in characteristic p. In his article, he proves a characterization of sympletic groups required for the identification of the Galois group of certain polynomials. The more abstract aspects come into play when considering the totality of Galois extensions of a given field. This leads to the study of absolute Galois groups and (profinite) fundamental groups. Haran and Jarden present a result on the problem of finding a group-theoretic characterization of absolute Galois groups. In a similar spirit, Boston studies infinite p-extensions of number fields unramified at p and makes a conjecture about a group-theoretic characterization of their Galois groups. He notes connections with the Fontaine-Mazur conjecture, knot theory and quantum field theory. Nakamura continues his work on relationships between the absolute Galois group of the rationals and the Grothendieck-Teichmüller group. Finally, Fried takes us on a tour of places where classical tropics like modular curves and j-line covers connect to the genus zero problems which was the starting point of the Guralnick-Thompson Conjecture. Audience This volume is suitable for graduate students and researchers in the field.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aAlgebraic geometry.
650 0 _aGroup theory.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aAlgebraic Geometry.
700 1 _aVoelklein, Helmut.
_eeditor.
700 1 _aShaska, Tanush.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387235332
830 0 _aDevelopments in Mathematics,
_x1389-2177 ;
_v12
856 4 0 _uhttp://dx.doi.org/10.1007/b101762
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c505930
_d505930