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Automorphic Forms and Shimura Varieties of PGSP(2005)  무료배송

 
지은이 : Flicker
출판사 : World Scientific
판수 : 1 edition
페이지수 : 340 pages
ISBN : 9812564039
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
   

 
The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings." This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,C) in SL(4, C). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum.
Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations.

To put these results in a general context, the book concludes with a technical introduction to Langlands’ program in the area of automorphic representations. It includes a proof of known cases of Artin’s conjecture.

Lifting Automorphic Forms of PGSp(2) to PGL(4):
Basic Facts
Trace Formulae
Lifting from SO(4) to PGL(4)
Lifting from PGSp(2) to PGL(4)
Fundamental Lemma
Zeta Functions of Shimura Varieties of PGSp(2):
Automorphic Representations
Local Terms
Real Representations
Galois Representations
Background:
On Automorphic Forms
On Artin’s Conjecture
Introduction to Partial Di...
-Zachmanoglou-
 
 
Real Analysis Modern Techn...
-Folland-
 
 
A First Course in Abstract...
-John B. Fraleigh-
 
 
   
 
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