Two lemmas on formal power series
Turkish Journal of Mathematics, cilt.23, sa.3, ss.435-440, 1999 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 23 Sayı: 3
- Basım Tarihi: 1999
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.435-440
- Anahtar Kelimeler: Coleman power serie, Formal groups, Formal power series, Local fields, Lubin-Tate theory
- Boğaziçi Üniversitesi Adresli: Evet
Özet
Let L be a local field and L̃ the completion of the maximal unramified extension of L. In this short note, we prove (I) the sequences (1″) 0 → OL[[X1, . . . , Xn]] → O L̃[[X1, . . . , Xn] → φL-1 OL̃[[X1, . . . , Xn]] → 0 and (2″) 1 → OL[[X1, . . . , X n]] → OL̃[[X1, . . . , Xn] →φL-1 OL̃[[X1, . . . , X n]] → 1 are exact, where θL is the Frobenius automorphism over L applied on the coefficients of OL̃[[X 1, . . . , Xn]], and θL - 1 respectively denotes the mapping α → αθL - α for (1″) and ∈ → ∈φL/∈ for (2″); (II) C○ (L̃, h) being the group the Coleman power series of degree 0, the sequence 1 → C○ (L, h) → C ○ (L̃, h) C○ (L̃, h) → 1 is exact, where C○ (L, h) = OL[[X]]x ∩ C ○ (L̃, h). © TÜBİTAK.