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Showing 1 to 6 of 6 for “"p-adic fields"”.
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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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The local-global principle in number theory
" p-adic fields provide remarkable, easy and natural solutions to problems which apparently have no relation to p-adic fields and which otherwise can be resolved, if at all, only by deep and arduous methods ". -- J. W. S. Cassels The first Local-Global Principle, formulated by Hasse in 1921, …
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Smooth ℓ-modular representations of unramified p -adic U(2, 1)(E/F)
Let E/F be an unramified quadratic extension of p-adic fields and G be the unitary group U(2, 1)(E/F). In this thesis we construct all ℓ-modular irreducible cuspidal representations of G by compact induction from irreducible representations of compact open subgroups of G. Under an assumption on the …
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Local Newforms and Spherical Characters for Unitary Groups
… even and odd dimensional unitary groups over p-adic fields. This definition is compatible with the one given by Atobe, Oi, and Yasuda in the odd dimensional case. Using the nonvanishing of the local spherical character at the test vector, we prove the existence of the representation containing …
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Families of p̳-adic Galois representations
… theory of finite slope subspaces to arbitrary p-adic fields, and then apply it to the generic fibers of Galois deformation spaces. I study the finite slope deformation rings in details by computing the dimensions of their Zariski cotangent spaces via Galois cohomologies. It turns out that the …