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Showing 1 to 20 of 84 for “"p-adic"”.
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A p-adic spectral triple
… continuous functions on the space of <em>p</em>-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative <em>D</em> on the tree. Our spectral triple satisfies the properties of a compact …
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The p-adic local langlands conjecture
Let k be a p-adic field. Split reductive groups over k can be described up to k- isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group of k. The Galois action on the based root datum is shared by members of an …
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p-adic L-functions of automorphic forms
… at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a construction by Spieß over totally real fields. It seems well-suited to generalize his proof of the …
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Iwasawa theory of p-adic Lie extensions
The Iwasawa theory of p-adic Lie groups investigates arithmetic objects above infinite field extensions of a number field k whose Galois group is a p-adic analytic group. The most prominent example (due to Serre) is produced by adjoining the p-torsion points of an elliptic curve defined over k …
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Counting supercuspidal representations of p-adic groups
Let F be a non-archimedean local �eld with residual characteristic p ~= 2. In this thesis we will deduce a formula for the number of irreducible supercuspidal representations of GLN(F), N C 1, with !�($F ) = 1 and level less than or equal to k. Following Blasco, we construct all irreducible …
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p-arithmetic cohomology and p-adic automorphic forms
… representations can be used to define *p*-adic automorphic forms and families of them (eigenvarieties). In particular, we are able to give constructions of these objects in many new cases, such as when the reductive group is not quasi-split at *p*. We also prove that these constructions are …
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On Selmer groups and factoring p-adic L-functions
… restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and a Kubota-Leopoldt p-adic L-function. We prove a result involving Selmer groups that along with Dasgupta's result is consistent …
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Advances in the theory of p-adic continued fractions
L'abstract è presente nell'allegato / the abstract is in the attachment
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Types and supercuspidal representations of p-adic symplectic groups
Let <i>F</i> be a non-archimedean local field and let <i>G</i> = <b>G</b>(<i>F</i>) be the <i>F</i>-points of a reductive group defined over <i>F</i>. Bushnell and Kutzko have described a strategy to classify the representations of <i>G</i> via the theory of types, which associates to each inertial …
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p-adic Heights of Heegner points on Shimura curves
… to Np, we give an explicit construction of the p-adic Rankin-Selberg L-function L_p(f_E,-) and prove that when the sign of its functional equation is -1, its central derivative is given by the p-adic height of a Heegner point on the abelian variety A associated to f. This p-adic Gross-Zagier …
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Multiplicative Orientations of K -Theory and P-Adic Analysis
… description involves producing measures on the p-adic units with certain moments. In his thesis, Ando produced a criterion for an orientation to be Hinfinity. His theorem is a condition on the induced formal group law. We connect these two classifications by producing measures of the type above …
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p-adic modular forms over Shimura curves over Q
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main conjecture has been greatly generalized to admissible p-adic Lie extensions, and provides a conjectural relationship between L-values of motives and their associated Selmer groups. A key …
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p-adic L-functions and the Geometry of Hida Families
<p><br />A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address …
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Canonical Invariants for Corresponding Residue Systems in P-Adic Fields
Let F be a finite extension of $\doubq\sb{p}$. Let L/F be a normal, totally ramified extension of degree $p\sp{2n}$ with ${\cal B}$ the maximal ideal of ${\cal D}\sb{\rm L}$. Suppose the Hilbert sequence for L/F has a unique breakpoint at $t$. That is, if ${\cal G}$ = Gal(L/F), then its Hilbert …
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Equivariance in Tannakian duality and plectic p-adic Hodge theory
… study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic isocrystals. We …
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Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.
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P-adic L-functions for elliptic curves over CM fields
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1983
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