Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
The Geometry and Cohomology of Some Simple Shimura Varieties. (AM-151), Volume 151
Michael Harris, Richard Taylor
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory.
The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary.
Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
Kundenbewertungen
Special case, Square root, Vector space, Residue field, Equivalence class, Embedding, Shimura variety, Monic polynomial, Elliptic curve, Abelian variety, Algebraically closed field, Modular curve, Dimension, Simple group, Coefficient, Hasse invariant, Artinian, Absolute value, Finite field, Local class field theory, Eigenvalues and eigenvectors, Variable (mathematics), Moduli space, Weil pairing, Bijection, Equivalence of categories, Canonical map, Cohomology, Weil group, Infinitesimal character, Existence theorem, Compactification (mathematics), Division algebra, Conjecture, Ring of integers, Direct limit, Galois group, Subset, Galois cohomology, Spectral sequence, Separable extension, Tate module, Inverse system, Sheaf (mathematics), Profinite group, Dimension (vector space), Algebraic group, P-adic number, Geometry, Maximal torus, Transcendence degree, Unitary group, Valuative criterion, Base change, Codimension, Lie algebra, Zariski topology, Function field, Integer, Prime number, Automorphic form, Corollary, Field of fractions, Generic point, Functor, Theorem, Isomorphism class