DAI HOC QUOC GIA HA N O I TRirOTVG DAI HOC KHOA HOC TlT NHIEN NGUYEN DUY TAN VE SO HOC VA DOr DONG DIEU GALOIS CUA NHOM LOY DON THEN TRUONG H A M DIA PHU0NG VA TOAN CUC Chuyen nganh: Dai so va ly thuyet so Ma so LUAN AN TIEN SI TOAN HOC NGU'dl HUONG DAN KHOA HOC PCS TS Nguyen Quoc ThSng OAl HOC QUOC GIA HA NOI •RUNG TAM THONG TIN THU VIEN HA NOI - 2008 Muc luc Md dau Mot so kien thurc chuan b| 0.1 Nhdm dai sdaffine 0.2 Nhdm luy don tr6n trudng dac so 0.3 Luge dd nhdm affine, luge nh 0.4 Ddi ddng diin Galois 0.5 Ddi ddng dieu phang 0.6 M6t sd khai niem va ky hieu hay dung ly thuye't trudng 26 Tinh toan anh ciia anh xa dja phirang hoa 1.1 Tinh toan anh ciia anh xa dia phuang hda 1.2 Mot vai ling dung 1.3 Mdt md rdng ciia Dinh ly 1.1.1 c 1.4 Ke't luan CLia Chuong Ddi dong dieu Galois cua nhdm luy dan sd chieu < tren trudng khong hoan thien 2.1 Mdt sd tinh toan nhdm ddi ddng d 2.2 Mdt di^u kifn du cho tinh v6 han 2.3 Ddi ddng di^u cua nhdm luy dan 2.4 Ke't luan ciia Chuong Ddi dong dieu Galois cua nhdm luy don sd chieu < p — tren trudng ham dja phuang va toan cue 3.1 Ddi ddng di6u Galois cua nhdm luy don tron tr6n trudng ham dia phuang 66 3.2 Ddi ddng di6a Galois cua nhdm luy don tron tren trudng ham toan cue 3.3 Vai ap dung ddi vdi nguyen ly dia phuong-toan cue 3.4 Ket luan cua Chuong Mot khSng djnh tuong tu cua Gia thuyet Serre va mot sd van de lien quan 4.1 Tinh tri^t tieu ciia nhdm ddi ddng dieu Galois thu" nha't 4.2 Phuong trinh xac dinh nhdm li 4.3 Ket luan cua Chuong Ket luan Danh muc cong trinh cua tac gia lien quan den luan an Tai lieu tham khao ... dong dieu Galois cua nhdm luy don sd chieu < p — tren trudng ham dja phuang va toan cue 3.1 Ddi ddng di6u Galois cua nhdm luy don tron tr6n trudng ham dia phuang 66 3.2 Ddi ddng di6a Galois cua... Mot vai ling dung 1.3 Mdt md rdng ciia Dinh ly 1.1.1 c 1.4 Ke't luan CLia Chuong Ddi dong dieu Galois cua nhdm luy dan sd chieu < tren trudng khong hoan thien 2.1 Mdt sd tinh toan nhdm ddi ddng... sdaffine 0.2 Nhdm luy don tr6n trudng dac so 0.3 Luge dd nhdm affine, luge nh 0.4 Ddi ddng diin Galois 0.5 Ddi ddng dieu phang 0.6 M6t sd khai niem va ky hieu hay dung ly thuye't trudng 26 Tinh