A Formal Analogue of Hilbert's Theorem 90

1985 ◽  
Vol 94 (4) ◽  
pp. 603
Author(s):  
R. Coleman
Keyword(s):  
Hilbert’S Theorem 90 ◽  
Formal Analogue

scholarly journals ON THE p-ADIC BINOMIAL SERIES AND A FORMAL ANALOGUE OF HILBERT'S THEOREM 90 – ADDENDUM

2014 ◽  
Vol 57 (1) ◽  
pp. 101-105
Author(s):  
PAVLOS TZERMIAS
Keyword(s):  
Glasgow Math ◽  
Binomial Series ◽  
Hilbert’S Theorem 90 ◽  
Formal Analogue

AbstractThe proof of Theorem 3.2 in [1] (P. Tzermias, On the p-adic binomial series and a formal analogue of Hilbert's Theorem 90, Glasgow Math. J.47 (2005), 319–326) contains two opaque claims. The necessary clarifications are provided here.

scholarly journals A group-theoretical version of Hilbert's theorem 90

2015 ◽  
Vol 47 (4) ◽  
pp. 704-714
Author(s):  
C. Quadrelli ◽  
Th. Weigel
Keyword(s):  
Hilbert’S Theorem 90

Hilbert's Theorem 90 and the Segal Conjecture for Elementary Abelian p-Groups

1985 ◽  
Vol 107 (4) ◽  
pp. 775 ◽  
Author(s):  
Stewart Priddy ◽  
Clarence Wilkerson
Keyword(s):  
Hilbert’S Theorem 90

scholarly journals Residues of intertwining operators for SO*6 as character identities

2010 ◽  
Vol 146 (3) ◽  
pp. 772-794 ◽  
Author(s):  
Freydoon Shahidi ◽  
Steven Spallone
Keyword(s):  
Quadratic Extension ◽  
The Other ◽  
Levi Subgroup ◽  
Intertwining Operators ◽  
Central Character ◽  
Supercuspidal Representation ◽  
Induced Representations ◽  
Intertwining Operator ◽  
Other Hand ◽  
Hilbert’S Theorem 90

AbstractWe show that the residue at s=0 of the standard intertwining operator attached to a supercuspidal representation π⊗χ of the Levi subgroup GL2(F)×E1 of the quasisplit group SO*6(F) defined by a quadratic extension E/F of p-adic fields is proportional to the pairing of the characters of these representations considered on the graph of the norm map of Kottwitz–Shelstad. Here π is self-dual, and the norm is simply that of Hilbert’s theorem 90. The pairing can be carried over to a pairing between the character on E1 and the character on E× defining the representation of GL2(F) when the central character of the representation is quadratic, but non-trivial, through the character identities of Labesse–Langlands. If the quadratic extension defining the representation on GL2(F) is different from E the residue is then zero. On the other hand when the central character is trivial the residue is never zero. The results agree completely with the theory of twisted endoscopy and L-functions and determines fully the reducibility of corresponding induced representations for all s.

Eusebius’ Canon Tables as a Paratext for Ordering Textual Knowledge

2019 ◽  
pp. 21-55
Author(s):  
Matthew R. Crawford
Keyword(s):  
Information Visualization ◽  
Second Century ◽  
Relational Categories ◽  
History Of ◽  
Textual Material ◽  
History Of Information ◽  
Navigational System ◽  
Fourfold Gospel ◽  
Formal Analogue

This chapter situates the Eusebian apparatus against the backdrop of the theory and history of paratexts and the theory and history of information visualization. It argues that Eusebius’ Canon Tables were a highly original paratext and a remarkably sophisticated instance of information visualization when compared to what preceded them. The closest formal analogue to the Canon Tables is shown to be the astronomical tables composed by Ptolemy in the second century. When seen in relation to the fourfold gospel, the Canon Tables are a paratext that orders the textual material of the gospels by organizing it into relational categories and providing the user with a navigational system when reading the corpus.

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