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Number theory --- Valued fields. --- p-adic fields. --- P-adic fields.
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Algebra --- p-adic fields --- Germs (Mathematics) --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Equivalence classes (Set theory) --- Functions --- Algebraic fields --- p-adic numbers --- p-adic fields. --- Germes (mathématiques) --- Représentations de groupes --- Représentations de groupes.
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"Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions over finite fields in a manner that is parallel to that of the classical hypergeometric functions. Using a comparison between the classical gamma function and its finite field analogue the Gauss sum, we give a systematic way to obtain certain types of hypergeometric transformation and evaluation formulas over finite fields and interpret them geometrically using a Galois representation perspective. As an application, we obtain a few finite field analogues of algebraic hypergeometric identities, quadratic and higher transformation formulas, and evaluation formulas. We further apply these finite field formulas to compute the number of rational points of certain hypergeometric varieties"--
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Group theory --- p-adic fields. --- Groupes p-adiques. --- Symplectic groups. --- Groupes symplectiques. --- Representations of groups. --- Représentations de groupes. --- p-adic fields --- Representations of groups --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebraic fields --- p-adic numbers
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Group theory --- Functional analysis --- Symplectic groups. --- Groupes symplectiques. --- p-adic fields. --- Groupes p-adiques. --- Representations of groups. --- Représentations de groupes. --- p-adic fields --- Representations of groups --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebraic fields --- p-adic numbers
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This book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.
Geometry, Algebraic. --- Finite fields (Algebra) --- p-adic fields. --- Algebraic fields --- p-adic numbers --- Modular fields (Algebra) --- Algebra, Abstract --- Galois theory --- Modules (Algebra) --- Algebraic geometry --- Geometry --- Symmetric domains. --- Domains, Symmetric --- Functions of several complex variables
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Group theory --- p-adic fields --- Hecke algebras --- Representations of groups --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebras, Hecke --- Group algebras --- Algebraic fields --- p-adic numbers --- Groupes symplectiques --- Représentations de groupes --- Hecke, Algèbres de --- Groupes symplectiques. --- Représentations de groupes. --- Hecke, Algèbres de.
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Singularities (Mathematics) --- p-adic fields --- p-adic groups. --- Functions, Zeta. --- Monodromy groups --- Geometry, Algebraic. --- Singularités (Mathématiques) --- Corps p-adiques --- Groupes p-adiques --- Fonctions zêta --- Groupes de monodromie --- Géométrie algébrique --- p-adic groups --- Functions, Zeta --- Geometry, Algebraic --- Singularités (Mathématiques) --- Fonctions zêta --- Géométrie algébrique
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