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Transcription
The ring BdR
The ring is defined as follows. Let denote the completion of . Let
So an element of is a sequence of elements
such that . There is a natural projection map given by . There is also a multiplicative (but not additive) map defined by , where the are arbitrary lifts of the to . The composite of with the projection is just . The general theory of Witt vectors yields a unique ring homomorphism such that for all , where denotes the Teichmüller representative of . The ring is defined to be completion of with respect to the ideal . The field is just the field of fractions of .
Fontaine, Jean-Marc (1982), "Sur Certains Types de Representations p-Adiques du Groupe de Galois d'un Corps Local; Construction d'un Anneau de Barsotti-Tate", Ann. Math., 115 (3): 529–577, doi:10.2307/2007012
Fontaine, Jean-Marc, ed. (1994), Périodes p-adiques, Astérisque, vol. 223, Paris: Société Mathématique de France, MR1293969
This page was last edited on 20 December 2023, at 09:04