Bộ sách luyện thi ETS 2023 LC&RC
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299,000₫
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The goal of this textbook is to introduce and study
automorphic representations, objects at the very core of the Langlands
Program. It is designed for use as a primary text for either a semester
or a year-long course, for the independent study of advanced topics, or
as a reference for researchers. The reader is taken from the beginnings
of the subject to the forefront of contemporary research. The journey
provides an accessible gateway to one of the most fundamental areas of
modern mathematics, with deep connections to arithmetic geometry,
representation theory, harmonic analysis, and mathematical physics. The
first part of the text is dedicated to developing the notion of
automorphic representations. Next, it states a rough version of the
Langlands functoriality conjecture, motivated by the description of
unramified admissible representations of reductive groups over
nonarchimedean local fields. The next chapters develop the theory
necessary to make the Langlands functoriality conjecture precise. Thus
supercuspidal representations are defined locally, cuspidal
representations and Eisenstein series are defined globally, and
Rankin-Selberg L-functions are defined to give a link between the global
and local settings. This preparation complete, the global Langlands
functoriality conjectures are stated and known cases are discussed. This
is followed by a treatment of distinguished representations in global
and local settings. The link between distinguished representations and
geometry is explained in a chapter on the cohomology of locally
symmetric spaces (in particular, Shimura varieties). The trace formula,
an immensely powerful tool in the Langlands Program, is discussed in the
final chapters of the book. Simple versions of the general relative
trace formulae are treated for the first time in a textbook, and a
wealth of related material on algebraic group actions is included.
Outlines for several possible courses are provided in the Preface.
Categories:Mathematics - Number Theory
Content Type:Books
Volume:300
Year:2024
Edition:1
Language:english
Pages:551
