Razrabotka metodov obosnovaniya gipotez formal'nykh teoriy Algebraicheskie mnogoobraziq, ciseau géométrique, prilozheniq

Tsel' nastoyashchey nebol'shoy knigi - vvesti chitatelya v obshirnuyu oblast' issledovaniy, posvyashchennuyu obosnovaniyu gipotez formal'nykh teoriy s ispol'zovaniem komp'yuternykh metodov. Ona formiruetsya shest' poslednikh desyatiletiy na osnove matematicheskoy logiki, teorii chisel, algebry, algebraicheskoy geometrii, analiza, chislennykh metodov i komp'yuternykh nauk. Sredi teoretiko-chislovykh, algebraicheskikh i arifmetiko-geometricheskikh ob"ektov, izuchaemykh v knige, prisutstvuyut formal'nye sistemy, diofantovy uravneniya, algebraicheskie krivye, prostranstva moduley, kriticheskie reshetki i opredeliteli. Priveden ryad sovremennykh konstruktsiy, pozvolyayushchikh komp'yuternoe issledovanie etikh ob"ektov. Izlozhenie sleduet ne vkusam i interesam avtora, a tselyam obosnovaniya gipotez, voznikshikh pri issledovanii klassicheskikh problem. V knige izlagayutsya kak nachal'nye, tak i fundamental'nye rezul'taty geometrii chisel i teorii algebraicheskikh mnogoobraziy. Kniga soderzhit otkrytye problemy i otvechayushchie im gipotezy.