<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings"^^ . "Consider the absolute Galois group $G_K$ of an extension $K$ of $\\mathbb{Q}_p$ finite degree $d$, and a finite field $\\mathbb{F}$ of prime characteristic $p$. \r\nFollowing Mazur [Maz89], we define the versal deformation ring $R_{\\overline{\\rho}}^\\psi$ with fixed determinant of a Galois representation $\\overline{\\rho}: G_K\\to GL_n(\\mathbb{F})$. \r\nThen for $n=2$ and $p>3$ our first main result states that $R_{\\overline{\\rho}}^\\psi$ is an integral domain so that the associated versal deformation space $\\mathfrak{X}(\\overline{\\rho})$ is irreducible. For this, we use the explicit relations of $R_{\\overline{\\rho}}^\\psi$ computed in [Boe00] and a commutative algebra criterion. We deduce from [Nak13] that for $n=2$ and any $K$ the benign crystalline points are Zariski dense in $\\mathfrak{X}({\\overline{\\rho}})$. This is expected to be useful for the surjectivity of the $p$-adic local Langlands correspondence.\r\nFurthermore, for arbitrary $n$ and $p$ we show that the refined quadratic parts of the relations of $R_{\\overline{\\rho}}^\\psi$ can be obtained cohomologically from a cup product and a Bockstein homomorphism if a certain lift of $\\overline{\\rho}$ exists.\r\nFollowing Chenevier [Che14], we construct the universal pseudodeformation ring $R_{\\overline{D}}^{univ}$ of an $n$-dimensional pseudorepresentation $\\overline{D}: \\mathbb{F}[G_K]\\to\\mathbb{F}$. \r\nMotivated by the result [Che11] on the equidimensionality of the generic fiber of the universal pseudorepresentation ring in characteristic $0$, our second main result says that the special fiber $\\overline{R}_{\\overline{D}}^{univ}$ of $R_{\\overline{D}}^{univ}$ is equidimensional of dimension $dn^2+1$ if $p>n$ or if $K$ does not contain a primitive $p^{th}$ root of unity $\\zeta_p$. In the latter case, if either $n>2$ or $n=2$ and $d>1$ we prove that the regular locus of $\\Spec\\overline{R}_{\\overline{D}}^{univ}$ consists of certain irreducible pseudodeformations and that $\\overline{R}_{\\overline{D}}^{univ}$ satisfies Serre's condition $R_2$."^^ . "2018" . . . . . . . "Ann-Kristin"^^ . "Juschka"^^ . "Ann-Kristin Juschka"^^ . . . . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (PDF)"^^ . . . "Ann-Kristin-2018-03-30.pdf"^^ . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (Other)"^^ . . . . . . "small.jpg"^^ . . . "Geometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings (Other)"^^ . . . . . . "indexcodes.txt"^^ . . "HTML Summary of #24224 \n\nGeometric Properties of Versal Deformation Rings and Universal Pseudodeformation Rings\n\n" . "text/html" . . . "510 Mathematik"@de . "510 Mathematics"@en . .