Sh af are v ich ▁formula ▁and ▁the ▁N ér on – O gg – Sh af are v ich ▁criter ion . ▁He ▁also ▁form ulated ▁the ▁Sh af are v ich ▁conject ure ▁which ▁stated ▁the ▁fin iten ess ▁of ▁the ▁set ▁of ▁Ab elian ▁vari eties ▁over ▁a ▁number ▁field ▁having ▁fixed ▁dimension ▁and ▁pres cribed ▁set ▁of ▁pr imes ▁of ▁bad ▁reduction . ▁This ▁conject ure ▁was ▁proved ▁by ▁G erd ▁F alt ings ▁as ▁a ▁step ▁in ▁his ▁proof ▁of ▁the ▁M ord ell ▁conject ure . ▁ ▁Sh af are v ich ▁was ▁a ▁student ▁of ▁Bor is ▁D ela un ay , ▁and ▁his ▁students ▁included ▁Y uri ▁Man in , ▁Alex ey ▁Par sh in , ▁Ig or ▁Dol g ache v , ▁Ev gen y ▁Gol od , ▁Alex ei ▁Kost rik in , ▁Ig or ▁A . ▁Kost rik in , ▁Sur en ▁A rak el ov , ▁G . ▁V . ▁B ely i , ▁Victor ▁Abr ash kin , ▁And rey ▁N . ▁Ty ur in , ▁and ▁Victor ▁Kol y v agin . ▁He ▁did ▁major ▁work ▁in ▁collaboration ▁with ▁I ly a ▁P iat et ski - Sh api ro ▁on ▁K 3 ▁surfaces . ▁He ▁was ▁a ▁member ▁of ▁the ▁Ser bian ▁Academy ▁of ▁Sciences ▁and ▁Arts ▁in ▁the ▁department ▁of ▁Mathemat ics , ▁Physics ▁and ▁Earth ▁Sciences . ▁In ▁ 1 9 6 0 ▁he ▁was ▁elected ▁a ▁Member ▁of ▁the ▁German ▁Academy ▁of ▁Sciences ▁Leopold ina