Japan - Korea International - Ring Theory symposium on Nagoya , - PDF document

0 The Oth China Japan - Korea International - Ring Theory symposium on Nagoya , August 26 - 37 , August 27 , 2019 , 9- 9.50 Singulier Hochschild cohomologie and the singularisez Category

1 Plan : 1 Hochschild hohomdogy . 2. Sang . Hochschild cohomologie and the main thm Application : 2 reconstruction thms With Zheng Hua ) 3. 1.tt#hid-byitstvimrykafieldlforsimpUcity ) A a k - algebra ( ) asso , with 1 non com , Htt * LA , A) Htt * IA ) = ed to Eilenberg Hochschild homology ( 1945 : attribut - MacLane ) = * CIA H , A) = - LA → Honda . - trompe LA . ) CIA , Al , A) → , A) - the .mg/AaA , A) → . . . . ) ) au [ ] , f11 ( aoobtfcab ) ta flb a , ? - Fab a com . alg We see : = 2- CA HUMA ) ) . HHYA e- Out a Liealg ) Berta ) . = identité bimodule Ae - Aa AM envebpinq algebra , a-ha - Eilenberg 4956 ) = Externe LA : algebra Cartan : cup product * ) : HH LA , A) HH MAI is grade d.com . Ger Men haha ll ) : 963 ) with È A = Unit in DIE modern argument : A a grand Lie algebra * t' HH (A) : Gerstein haber brachet is . ) Getz 42 : ( ) , u , bruce op 1er - Gones U CHA Bo - algebra is a 4981 ) : By ftp.spaeeX CÉGCX , Z B : Banes ) is bruce op . ( ) Kadeiohvili 1988 : Holt Yu _ rez - Z ± → ¥ c suiv , Rks D The By . certains all the info , ce ] = chez 7 niez - str [ e. g. c , . zes from k - algebra s to k - catégories ( 2) The canon . generali ) and to Mitchell 1972 différentiel grade d E- G) catégories HH * ( A) Ing (A) ⇐ HHAÈÏMODA Thon ( ) : Lower - Vanden Bergh 2005 ) - HH Htt * * ( 8dg At ( this lifts to the Bx - level ) , K 2003 . Not Moda a { DA - DMODA ) A - modules 3 , = unbocendeddene.at ah Cright . : . Ddg A = canonical dg entrainement of DA . , we get Rk : En particulier 2- (A) - Z ( Dag A) . " ( Krause - le , 20h ) = Kkk 2- ( DA ) is pathologie " 2- ( D' ) Cheikh e. g. ,

Z 2.Tate-tdcohomologyAari.gl t Nœth . algebra ( for nmplicity ) = 4 - modules } fin mod A . gen . A D' = Db A ( A) mod Xe D' = { ) IX qis to a bded complex of forger per A lmoda : modules } . png = D' Alpert sg (A) ) 8 table derivedcat . ( 1986 Buchwcitz = = singularity category ( ) Orlov 2003 - Assume Ae is also Noethérien . Def : Sing = Extsgcae = HHISGIA ) , Hooks , HA ) - whom . . Rh : HHIgtalisgradedcom.la/thoceghsgCA9isnotmonoidaL ) . ) : a) Httsg IA Thm ( Zheng fang Wang Canonical ( ) Gerstenhaber brochet Kass ) carrées a butin tricote ! u o c , A) computing HHÎGIAI b) There is a can . Bo Çg CA 12018 ) . - alg Beech Weitz : . _ ) à HH * l sga HHËLA Main Thm : , A) as gradedalgebras . Gong : : This room , lifts to the - level Bo . True for A = KOYCQ Chen - Li - Wang ) : Thm ( , R , where Q is a prit quitter wlonnksnor sources - Dogs modal , S = sgag LA Isom , in the main thm : M ) ( We have dg furetas : M # S , po i ← 0 A . org Ë @ ( ⑨ LA AP ) DIA roman Y cpcopt | - ⇒ Des ) .sn qq Cae - - - - - - - - - - - - - - - - - - A 1- Idg indexes an Dom . the on V Yone da algésiras .

3 with Zhèng Huâ ) ms ( 3.Applicznchn.tn _ , xD → R = 51ff . sang T1 : E- et ) isol x , , . . Then R is de terminal by Miss R and s.gg CRI . = Htlosg ( = 8Kf , Ex Zlsgdg R ) . _ , Ex . ) Pro of : ) R Tgurinaalg . of R mec > . . , Buch weitz ✓ BACH drink and the Ty urina a ) détermine R ( Mather , Grenet - Pham 2017 G. you 1982 . V - local - R a complete . compound du Val Ang [ , a generis hyper pleine section is du Val I idol 3- clim . , normal . f :X → Spec R smooth min . model contractiez a tree of rat . cuves Donovan - Wcmyss , 2013 the associated contractionalgebra ( ) [ M . fibre représente the NC defo of the axe M = fac ( ) ( Vanden Bergh ) , W Q = image of W in J HH . (1) Tlmt : The de . class of 11 , F) . eq Me termines R . Donovan - Wemyss long : that the : D Rks . class of 1 ↳ détermines R deo . eq . sg CR ) = Ca 2) ( ) . cluster category Amiot 2009 = gen , w