WebOct 2, 2024 · topology on the ring of Witt vectors in the theory of period rings of Fontaine. For a p -adic field K with perfect residue field k, we know the standard construction of the … WebFontaine's period rings. In mathematics, Fontaine's period rings are a collection of commutative rings first defined by Jean-Marc Fontaine that are used to classify p-adic Galois representations. [1] 5 relations: Commutative ring, Galois module, Jean-Marc Fontaine, Mathematics, Witt vector.
THE FARGUES{FONTAINE CURVE AND DIAMONDS [d’apr es …
WebQb is an algebraically closed eld whose ring of integers is denoted by O C p. If Ais a perfect F p-algebra, what means that [x7!xp] is an automorphism, we can de ne its ring of Witt … 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 defin… shp asx share price
Fontaine
Web2.1. Relative Period Rings 8 2.2. Relative Fontaine-Laffaille Modules 10 2.3. Torsion Representations associated to Fontaine-Laffaille Modules 15 3. Fontaine-Laffaille data and torsion crystalline cohomology 19 3.1. The case d “ 1 19 3.2. The general case 22 4. Construction of Relative Fontaine-Laffaille data and the comparison map 24 4.1 ... WebFirst, consider the case of p -adic representations of the absolute Galois group G K, where K denote a p -adic field. Among all these representations, we can distinguish some of them, namely those which are Hodge-Tate, de Rham, semistable or crystalline. This is due to Fontaine who constructed some period rings : B H T, B d R, B s t and B c r y s. WebMay 26, 2024 · Fontaine defines in "Le corps des périodes p-adiques" (see loc.cit, remark 1.2.4. (c)) as the completion of $\mathcal {O}_K\otimes_ {W (k)}W (\mathcal {O}_C^ … shp bd topo