A invariance infinite space thanks to Bott - PDF document

New models for motivic K theory spectra Universality of algebraic K theory от Joachim Denis Burt Мая j.eu Bachmann recent Тот progress Goal for today understand universal property new a and hermitian at K theory and its applications alg К perfect base field Into К law Vat defined К SHIP Spe as where stack vet the preheat of Ею spaces is smf Xtsgpdotub.ae Х Some features of К descent Zarate ЙЁ ĸм Ёĸахту ним A Иру invariance infinite РДоор space thanks to Bott К tank periodicity К finite flat finite flat f X transfers induced by f КМ Иесыху Vatted Их Moral К is universal heaves pres among these features with Simi Spc data properties

precise formulation Towards in His shes of spaces оиаĸ SULU Р spectra in A SH spectra Цру iv М V property Диман gftlatf.LI where eschn.EE САМУ К он 2CanfHatCk is with cat 2.1 a maps у XESmfh.gl Р connective spectrum representing К so we have kgl.rs Ки under Ree 5461 SH equivalence of Main Thur Тот There's an us 1 SHEIK d Ед symm.mou.tt Модурнажд й д 2 dark 8414 e 3 dark р р sense h.gl represent the universal this In generalised cohomology theory with finite flatters motivic of two The consists parts proof fr latsalnies.pe veetsp t.kgl 9 def transfers A equivalence он affine universal group like Alin sheaf the is Мр Кдв so Of flat transfer finite Ею spaces with deduce lot of general then main using a motivic theory motivic recognition principle ЕНКУ transfers По cancellation then forth etc

istedaicelkiwudueefIlltalkabout since is only used Ю Ihfa.ct the ван assumption The main И base works ingredient is over Ueda даааа the following Пдд is an A equivalence О Е Е extension что square Proof Fifa Veda The inverse A А is Ард Need to show FFIatd vectd F.FI disA eguir По О toidl.FR А СЯН define At explicit homotopy along an Reesalgebras ring S algebra with increasing filtration А с ДЕ A Aj с Анд Then АПА i Као with Ait К A is graded sets algebra grading comes вдздай 794 A.de and дна НАШ RLAKt.y are flat overs all If so is ММ aerSE.tl даа Ауд this to canonical filtration the We apply of any с А AEFFIatd.IS 11 5.2 Ад Ао S Ад We МА get А ЧАЩЕ f here чего product natural and extends the to so Анна is пиар KFIatfakaffhtdstr Их FFlat ra.fm S d provides the A Иду between АНАРХИЯ ida.am which Maps A fatty

that With this t.hn не роĸ он offices F Flats Vector Медиĸ is an that FFlatsp zxr f.la using tF йЕН a Ёа a later A that and r FIatd Venta veotdquareofo.net 9 1 ibid intact It's more subtle where Vectis он because square zeroed doesn't commute пар with и пару Applications Hilbert scheme model for К As нее но Их Vector zxffla.tn ĸ Мр Кде АЖ ТК forgetful The вор пар Flat A ее a taffies Hild is да an и space of embeddings into this Аĸсой Intl 2 ща 't T 2 fit w Hills АРТ Хх Hills САЕ So ĸ e А А its A Кру type is ах E space because то you in schemes disjoint make any closed sub can

spaces of hgt Higher show that for Хевце More generally can не ttE.x 4te яйце Каĸ t.x.IE Ею via I corrfflatf.LA and hilbCAI analogue of be thought of as This can equivalent to Segal MCku Ei.isweahlg configuration space АХ др of labelled the labelled by pairwise where points inat.pe orthogonal are embedded into a sp and Ею she 0 complex so that is defined you sumv.gs when pts collide a forgetful пар have In we our case ю РП Hillock бути НИКАК syn A support х degree i iii fiF ЕЁ n 1 в methods that thefiber show by We similar can i Е ХИ distinct of this over say Кар is not equivalent drive i i Р i We get Hilbert sohu.me models Бы Upshot over any perfect field Gait need СЕЗ Мы ftp.kgl но and Кдурена to compute steeeuodalg.in Dream Use this char Р