<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws"^^ . "We give an introduction to the theory of pseudorepresentations of Taylor, Rouquier, Chenevier and\r\nLafforgue. We refer to Taylor’s and Rouquier’s pseudorepresentations as pseudocharacters. They are\r\nvery closely related, the main difference being that Taylor’s pseudocharacters are defined for a group,\r\nwhere as Rouquier’s pseudocharacters are defined for algebras. Chenevier’s pseudorepresentations are\r\nso-called polynomial laws and will be called determinant laws. Lafforgue’s pseudorepresentations are a\r\ngeneralization of Taylor’s pseudocharacters to other reductive groups G, in that the corresponding notion\r\nof representation is that of a G-valued representation of a group. We refer to them as G-pseudocharacters.\r\n\r\nWe survey the known comparison theorems, notably Emerson’s bijection between Chenevier’s determinant\r\nlaws and Lafforgue’s GL(n)-pseudocharacters and the bijection with Taylor’s pseudocharacters away from\r\nsmall characteristics.\r\n\r\nWe show, that duals of determinant laws exist and are compatible with duals of representations. Analogously,\r\nwe obtain that tensor products of determinant laws exist and are compatible with tensor products\r\nof representations. Further the tensor product of Lafforgue’s pseudocharacters agrees with the tensor\r\nproduct of Taylor’s pseudocharacters.\r\n\r\nWe generalize some of the results of [Che14] to general reductive groups, in particular we show that\r\nthe (pseudo)deformation space of a continuous Lafforgue G-pseudocharacter of a topologically finitely\r\ngenerated profinite group Γ with values in a finite field (of characteristic p) is noetherian. We also show,\r\nthat for specific groups G it is sufficient, that Γ satisfies Mazur’s condition Φ_p.\r\n\r\nOne further goal of this thesis was to generalize parts of [BIP21] to other reductive groups. Let F/Qp\r\nbe a finite extension. In order to carry this out for the symplectic groups Sp2d, we obtain a simple and\r\nconcrete stratification of the special fiber of the pseudodeformation space of a residual G-pseudocharater\r\nof Gal(F) into obstructed subloci Xdec(Θ), Xpair(Θ), Xspcl(Θ) of dimension smaller than the expected dimension\r\nn(2n + 1)[F : Qp].\r\n\r\nWe also prove that Lafforgue’s G-pseudocharacters over algebraically closed fields for possibly nonconnected\r\nreductive groups G come from a semisimple representation. We introduce a formal scheme\r\nand a rigid analytic space of all G-pseudocharacters by a functorial description and show, building on\r\nour results of noetherianity of pseudodeformation spaces, that both are representable and admit a decomposition\r\nas a disjoint sum indexed by continuous pseudocharacters with values in a finite field up to\r\nconjugacy and Frobenius automorphisms.\r\n\r\nAt last, in joint work with Mohamed Moakher, we give a new definition of determinant laws for symplectic\r\ngroups, which is based on adding a ’Pfaffian polynomial law’ to a determinant law which is invariant under\r\nan involution. We prove the expected basic properties in that we show that symplectic determinant laws\r\nover algebraically closed fields are in bijection with conjugacy classes of semisimple representation and\r\nthat Cayley-Hamilton lifts of absolutely irreducible symplectic determinant laws to henselian local rings\r\nare in bijection with conjugacy classes of representations. We also give a comparison map with Lafforgue’s\r\npseudocharacters and show that it is an isomorphism over reduced rings."^^ . "2023" . . . . . . . "Julian Christian"^^ . "Quast"^^ . "Julian Christian Quast"^^ . . . . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (PDF)"^^ . . . "Dissertation_Quast_FINAL.pdf"^^ . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Deformation theory of G-valued pseudocharacters and symplectic determinant laws (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #33231 \n\nDeformation theory of G-valued pseudocharacters and symplectic determinant laws\n\n" . "text/html" . . . "000 Allgemeines, Wissenschaft, Informatik"@de . "000 Generalities, Science"@en . . . "500 Naturwissenschaften und Mathematik"@de . "500 Natural sciences and mathematics"@en . . . "510 Mathematik"@de . "510 Mathematics"@en . .