03259oam 2200685I 450 991081550360332120230802004329.00-429-06761-51-283-59620-297866139086501-4665-0193-610.1201/b11315 (CKB)2550000000079197(EBL)830246(OCoLC)773034262(SSID)ssj0000581416(PQKBManifestationID)11370656(PQKBTitleCode)TC0000581416(PQKBWorkID)10531248(PQKB)10632004(MiAaPQ)EBC830246(Au-PeEL)EBL830246(CaPaEBR)ebr10522560(CaONFJC)MIL390865(EXLCZ)99255000000007919720180331d2012 uy 0engur|n|---|||||txtccrLectures on N_X (p) /Jean-Pierre SerreBoca Raton, Fla. :CRC Press,2012.1 online resource (168 p.)Research notes in mathematics ;v. 11An AK Peters book.1-4665-0192-8 Includes bibliographical references.Front Cover; Contents; Preface; Conventions; Chapter 1. Introduction; Chapter 2. Examples; Chapter 3. The Chebotarev Density Theorem for a Number Field; Chapter 4. Review of l-adic Cohomology; Chapter 5. Auxiliary Results on Group Representations; Chapter 6. The l-adic Properties of NX(p); Chapter 7. The Archimedean Properties of NX(p); Chapter 8. The Sato-Tate Conjecture; Chapter 9. Higher Dimension: the Prime Number Theorem and the Chebotarev Density Theorem; ReferencesThis book presents several basic techniques in algebraic geometry, group representations, number theory, -adic and standard cohomology, and modular forms. It explores how NX(p) varies with p when the family (X) of polynomial equations is fixed. The text examines the size and congruence properties of NX(p) and describes the ways in which it is computed. Along with covering open problems and offering simple, illustrative examples, the author presents various theorems, including the Chebotarev density theorem and the prime number theorem--Provided by publisher.The main topic involves counting solutions mod p of a system of polynomial equations, as p varies. The book is based on a series of lectures presented by the author in Taiwan. Using this idea, Serre visits algebra and number theory and asks some non-standard questions, especially on group representations--Provided by publisher.Research notes in mathematics ;11.PolynomialsNumber theoryRepresentations of groupsCohomology operationsPolynomials.Number theory.Representations of groups.Cohomology operations.512.9/422MAT022000bisacshSerre Jean-Pierre1926,1700693MiAaPQMiAaPQMiAaPQBOOK9910815503603321Lectures on N_X (p)4083877UNINA