相對(duì)K-,1-,K-,2-和代數(shù)整數(shù)環(huán)的K-,2-.pdf

1、中國科學(xué)技術(shù)大學(xué)博士學(xué)位論文相對(duì)KK和代數(shù)整數(shù)環(huán)的K姓名：郭學(xué)軍申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：馮克勤宋光天2000.3.12000年中國科學(xué)技術(shù)大學(xué)博士學(xué)位論文第ii頁=；=#==口======；===================；=====一AbstractAlgebraicK，theorystartedfromGrothendiecksproofofhisgeneralizedRiemannRochtheoremin

2、I_937Thebeginningsofgeneralconstructionsandmathematicalsynthesisofalgebraicftheoryemergedatearlyt970sFromthenonchesubjecthastakenonarichlifeofhisownandfindapplicationsinmanyareasofalgebraicgeometry，algebraictopologyC。alg

3、ebraclassicaigroups，representationtheory，numbertheoryandanalysisManyFieldsviedalistsuch碣AGrothendieckJPSerreJMiinorDQuillen“l(fā)domanyimportantworksinthissubjectThisthesisconcernsrelativeⅣlandrelativeK2groupsandK2groupsoFal

4、gebraicintegersringsFirstlyweprovethatKL(R，)20。(R，，1／v(R，1ifRsatisfiedthestablerangelconditionhl(R，1=￡’(R，)／VfR，)whereV(R，)isasubgroupofr(R，)generatedby“((1d6一口dcdtabcdhl—dc十dQ6ndcba)一1：Ⅱ∈，6∈R，c∈，d∈，1下B6口d上cdabcd∈￡‘(R，)M

5、oreoverwegivemoreconcreteresu[tsofthesemiperfectringsand、B、ringsSecondlyweconsidertherelative^‘2groupsⅣ2(R，)IfRanditsideal，satisfiedtheconditionCSR2fR，)fieforanynbj，satisfiedⅡR一(L中6)R=尺，thereexists￡∈0(R，f)suchthatⅡ一(1—61

6、￡∈￡’(R，))then^’2(R，)isgeneratedbyelementsoftypeD(R，)andC’fR，)FinallyweconsidertheKgroupsofalgebraicintegersringsWegiveamethodtofindrelativelysmallmsuchthatK20F2ker(鞏K1F—ff女‘㈦)。蘭jjxSoitcansimplifythecomputionAsapplication