
bogomolov anumaanam

ganithashaasthrathil, ganitha jyaamithiyile maanin-mumford anumaanathe saamaanyavalkkarikkunna beejaganita vakrangalekkurichulla ganitha jyamithiyil feder bogomolovinte perilulla oru anumaanamaan bogomolov anumaanam. 1998ll immaanuval ulmoy shau-vuu shang eee anumaanam theliyichu. 1998ll shang general abelian enangalude kooduthal saamaanyavalkkaranam theliyichu.
prasthavana.
c" ennathu "k" enna samkhyaasampradeshathil nirvachichirikkunna "g" janussinte oru beejaganita vakramayirikkatte, soothravaakyam _ 1 ennathu "k" nte beejaganita bandhathe soochippikkatte, athinte jacobian inamaaya "j"-ll "c" ennathinte ulcherkkal nischayikkatte, koodaathe soothravaakyam _ 2 ennathu mathiyaya samamithiyulla oru vibhajakavumaayi bandhapetta "j"-ll neron-tettu uyarathe soochippikkatte. appol oru formula _ 3 nilavilundu, athaayath settu
p" oru tortion poyintaanengil maathram formula 5 aayathinal, bogomolov anumaanam maanin-mumpord anumaanathe saamaanyavalkkarikkunnu.
thelivu.
1998ll immaanuval ulmoy shau-vuu shang chernnaanu yadhaartha bogomolov anumaanam theliyichathu.
saamaanyavalkkaranam.
1998-ll shang thaazhepparayunna saamaanyavalkkaranam theliyichu
a" ennathu "k" ennathil nirvachichirikkunna oru abelian inamaayirikkatte, koodaathe formula _ 2 ennathu mathiyaya samamiti vibhajakavumaayi bandhapetta "a"-leeii neron-tettu uyaramayirikkatte. a" ennathinte abelian upavibhaagathinte tortion pooyint vivarthanam aanenkil oru subveratti formula _ 7 neey "tortion subveratti" ennu vilikkunnu. x" oru tortion subvariaty allengil, settu cheiyunna oru formula _ 3 undu.