By Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight
The notes during this quantity correspond to complicated classes held on the Centre de Recerca Matemàtica as a part of the study software in mathematics Geometry within the 2009-2010 educational year.
The notes through Laurent Berger offer an creation to p-adic Galois representations and Fontaine jewelry, that are specifically worthwhile for describing many neighborhood deformation jewelry at p that come up evidently in Galois deformation theory.
The notes by means of Gebhard Böckle supply a accomplished direction on Galois deformation idea, ranging from the foundational result of Mazur and discussing intimately the speculation of pseudo-representations and their deformations, neighborhood deformations at areas l ≠ p and native deformations at p that are flat. within the final section,the result of Böckle and Kisin on displays of world deformation jewelry over neighborhood ones are discussed.
The notes by way of Mladen Dimitrov current the fundamentals of the mathematics concept of Hilbert modular kinds and types, with an emphasis at the learn of the pictures of the hooked up Galois representations, on modularity lifting theorems over absolutely genuine quantity fields, and at the cohomology of Hilbert modular kinds with quintessential coefficients.
The notes via Lassina Dembélé and John Voight describe tools for appearing particular computations in areas of Hilbert modular kinds. those equipment depend upon the Jacquet-Langlands correspondence and on computations in areas of quaternionic modular types, either for the case of sure and indefinite quaternion algebras. a number of examples are given, and purposes to modularity of Galois representations are discussed.
The notes via Tim Dokchitser describe the evidence, got via the writer in a joint undertaking with Vladimir Dokchitser, of the parity conjecture for elliptic curves over quantity fields below the idea of finiteness of the Tate-Shafarevich crew. The assertion of the Birch and Swinnerton-Dyer conjecture is incorporated, in addition to a close research of neighborhood and international root numbers of elliptic curves and their classification.
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Extra resources for Elliptic Curves, Hilbert Modular Forms and Galois Deformations (Advanced Courses in Mathematics - CRM Barcelona)
Elliptic Curves, Hilbert Modular Forms and Galois Deformations (Advanced Courses in Mathematics - CRM Barcelona) by Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight