Baker-Fluckiger E., Lewis D., Raniki A. - Quadratic Forms and their Applications.pdf

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QuadraticForms
andTheirApplications
ProceedingsoftheConferenceon
QuadraticFormsandTheirApplications
July5{9,1999
UniversityCollegeDublin
EvaBayer-Fluckiger
DavidLewis
AndrewRanicki
Editors
PublishedasContemporaryMathematics272,A.M.S.(2000)
vii
Contents
Preface
ix
Conferencelectures x
Conferenceparticipants xii
Conferencephoto xiv
Galoiscohomologyoftheclassicalgroups
EvaBayer-Fluckiger 1
Symplecticlattices
Anne-MarieBerg e 9
Universalquadraticformsandthe¯fteentheorem
J.H.Conway 23
OntheConway-Schneeberger¯fteentheorem
ManjulBhargava 27
OntraceformsandtheBurnsidering
MartinEpkenhans 39
EquivariantBrauergroups
A.Fr Ä ohlichandC.T.C.Wall 57
Isotropyofquadraticformsand¯eldinvariants
DetlevW.Hoffmann 73
Quadraticformswithabsolutelymaximalsplitting
OlegIzhboldinandAlexanderVishik 103
2-regularityandreversibilityofquadraticmappings
AlexeyF.Izmailov 127
Quadraticformsinknottheory
C.Kearton 135
BiographyofErnstWitt(1911{1991)
InaKersten 155
viii
Genericsplittingtowersandgenericsplittingpreparation
ofquadraticforms
ManfredKnebuschandUlfRehmann 173
Localdensitiesofhermitianforms
MauriceMischler 201
NotestowardsaconstructiveproofofHilbert'stheorem
onternaryquartics
VictoriaPowersandBruceReznick 209
Onthehistoryofthealgebraictheoryofquadraticforms
WinfriedScharlau 229
Localfundamentalclassesderivedfromhigher K -groups:III
VictorP.Snaith 261
Hilbert'stheoremonpositiveternaryquartics
RichardG.Swan 287
Quadraticformsandnormalsurfacesingularities
C.T.C.Wall 293
ix
Preface
Thesearetheproceedingsoftheconferenceon\QuadraticFormsAnd
TheirApplications"whichwasheldatUniversityCollegeDublinfrom5thto
9thJuly,1999.Themeetingwasattendedby82participantsfromEurope
andelsewhere.Therewere13one-hourlecturessurveyingvariousappli-
cationsofquadraticformsinalgebra,numbertheory,algebraicgeometry,
topologyandinformationtheory.Inaddition,therewere22half-hourlec-
turesonmorespecializedtopics.
Thepaperscollectedtogetherintheseproceedingsareofvarioustypes.
Someareexpandedversionsoftheone-hoursurveylecturesdeliveredatthe
conference.Othersaredevotedtocurrentresearch,andarebasedonthe
half-hourlectures.Yetothersareconcernedwiththehistoryofquadratic
forms.Allpaperswererefereed,andwearegratefultotherefereesfortheir
work.
ThisvolumeincludesoneofthelastpapersofOlegIzhboldinwhodied
unexpectedlyon17thApril2000attheageof37.Hisuntimelydeathisa
greatlosstomathematicsandinparticulartoquadraticformtheory.We
shallmisshisbrilliantandoriginalideas,hisclarityofexposition,andhis
friendlyandgood-humouredpresence.
TheconferencewassupportedbytheEuropeanCommunityunderthe
auspicesoftheTMRnetworkFMRXCT-97-0107\Algebraic K -Theory,
LinearAlgebraicGroupsandRelatedStructures".Wearegratefultothe
MathematicsDepartmentofUniversityCollegeDublinforhostingthecon-
ference,andinparticulartoThomasUngerforallhisworkontheT E Xand
web-relatedaspectsoftheconference.
EvaBayer-Fluckiger,Besan»con
DavidLewis,Dublin
AndrewRanicki,Edinburgh
October,2000
x
Conferencelectures
60minutes.
A.-M.Berg e, Symplecticlattices.
J.J.Boutros, Quadraticformsininformationtheory.
J.H.Conway, TheFifteenTheorem.
D.Hoffmann, Zerosofquadraticforms.
C.Kearton, Quadraticformsinknottheory.
M.Kreck, Manifoldsandquadraticforms.
R.Parimala, Algebraswithinvolution.
A.Pfister, ThehistoryoftheMilnorconjectures.
M.Rost, Oncharacteristicnumbersandnormvarieties.
W.Scharlau, Thehistoryofthealgebraictheoryofquadraticforms.
J.-P.Serre, Abelianvarietiesandhermitianmodules.
M.Taylor, GaloismodulesandhermitianEulercharacteristics.
C.T.C.Wall, Quadraticformsinsingularitytheory.
30minutes.
A.Arutyunov, Quadraticformsandabnormalextremalproblems:some
resultsandunsolvedproblems.
P.Balmer, TheWittgroupsoftriangulatedcategories,withsomeapplica-
tions.
G.Berhuy, Hermitianscaledtraceformsof¯eldextensions.
P.Calame, Integralformswithoutsymmetry.
P.Chuard-Koulmann, Elementsofgivenminimalpolynomialinacentral
simplealgebra.
M.Epkenhans, OntraceformsandtheBurnsidering.
L.Fainsilber, Quadraticformsandgasdynamics:sumsofsquaresina
discretevelocitymodelfortheBoltzmannequation.
C.Frings, SecondtraceformandT 2 -standardnormalbases.
J.Hurrelbrink, Quadraticformsofheight 2 anddi®erencesoftwoP¯ster
forms.
M.Iftime, Onspacetimedistributions.
A.Izmailov,2 -regularityandreversibilityofquadraticmappings.
S.Joukhovitski, K-theoryoftheWeiltransferfunctor.

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