Lectures on Nx(p)

by Serre, Jean-Pierre

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Title Statements

Full title :Lectures on Nx(p).

Edition Statements

Publication Date:2012.

Publication Statements

Publisher(s):CRC Press
Place of Publication:Boca Raton
Language:eng
Publication Date:2012.

The Physical Object

Description:163 blz. ; : .. cm.

Edition Identifiers

ISBN:9781466501928, 1466501928
oclc:ocn840455826

Machine generated contents note: 1.1.Definition of Nx (p): the affine case -- 1.2.Definition of Nx (p): the scheme setting -- 1.3.How large is Nx (p) when p->infinity -- 1.4.More properties of p->Nx (P) -- 1.5.The zeta point of view -- 2.1.Examples where dim X(C) = 0 -- 2.2.Examples where dim X(C) = 1 -- 2.3.Examples where dim X(C) = 2 -- 3.1.The prime number theorem for a number field -- 3.2.Chebotarev theorem -- 3.3.Frobenian functions and frobenian sets -- 3.4.Examples of S-frobenian functions and S-frobenian sets -- 4.1.The l-adic cohomology groups -- 4.2.Artin's comparison theorem -- 4.3.Finite fields: Grothendieck's theorem -- 4.4.The case of a finite field: the geometric and the arithmetic Frobenius -- 4.5.The case of a finite field: Deligne's theorems -- 4.6.Improved Deligne-Weil bounds -- 4.7.Examples -- 4.8.Variation with p -- 5.1.Characters with few values -- 5.2.Density estimates -- 5.3.The unitary trick -- 6.1.Nx(p) viewed as an l-adic character -- 6.2.Density properties -- 6.3.About Nx(p)-Ny(P) -- 7.1.The weight decomposition of the l-adic character hx -- 7.2.The weight decomposition: examples and applications -- 8.1.Equidistribution statements -- 8.2.The Sato-Tate c…

Subjects

Cohomology operations Number theory Opérations cohomologiques Polynômes polynomials Représentations de groupes Representations of groups Théorie des nombres