The action of SL2 on abelian varieties

Arnaud Beauville

Description

The action of SL2 on abelian varieties Arnaud Beauville Universite de Nice Bar Ilan, May 2008 Arnaud Beauville The action of SL2 on abelian varieties

• hard lefschetz


• sl2


• bar ilan


• sl2 ??


• universite de nice

Sujets

• Beauville
• Bar-Ilan University
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Nombre de lectures: 9
• Langue: English

Extrait

dueBrAanllTeuaivontiachena 2 oSLofavnailebseiteir

action

The

varieties

ofSL 2 on abelian

Universite´deNice

Arnaud Beauville

Bar Ilan, May 2008

Arnaud

Beauville

The

action

on

abelian

varieties

Synopsis

SL

of

Aut(A)

? 

2

// N N  ? N N N N & 2 N & LS r(A) ∩ Cor t(A) // Au )A(rroC:tseretnIalritoncfuontsac,)A( A(HC..,)eh,. vainanrioftsH ∗ A: htseseapec.s nO ∗ H nceactionofSL 2 on 2 LSfonoieLdraH⇒⇐ascl):(Actlacasi aswtigevvdresiet etz.fsch (A):OnCH ct:Anoio z.et teNo eLdrhcsfnoisaHfo K¨unnemadyknown(A(a)rlaeSf 2 LnoHC .)kuhchsiloP ,nn

SL 2

ut / A)(A // ySonspsi LS ? 2 /  ostnairavnilairo ,.A)H( , C A) ∗ (:HfA:toCreseItnunctsonf)actrr(A alc:cissHnO . )A( ∗ SLof⇒H 2 ⇐acalonti caitnofo..h,neecsespacesSL 2 onthe ehztfecs :ecAN . to rsioedveardLnofHvig:)A(Htsiwtase scefdLar nC . O tzhe ku.) rAandueBuaiv nnemann, Polishch erlakydanwonu¨K(ontiSLofnC 2 oA)H(

SL 2

? Aut(A) N N N N N N ∩ N && Corr(A)

eisetrivaanlibena 2 oLSfonoitcaehTell

Olacissalc:)A( ∗ Hn zt N .cseh cAitto:eSL 2 oonofA)alnCH(onkydaernnu¨K(nw Po n,anem ukchshli caitnofoLS⇐ 2 H⇒radLefschetz. OnCH(g:)AseviiwtadetsrsvenoioarfHefdL fonoo 2 LSehTeitcaauBellviAr ). udnas

SL 2 ?  // Aut(A) N N N N N N N && ∩ Corr(A)

Interest:Corr(A) acts on functorial invariants ofA:H ∗ (A), CH(A), ... , hence action ofSL 2 on these spaces.

varietienabelian ut(A) LS ? 2 / A / ySonspsi