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Creators/Authors contains: "Park, Chol"

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  1. ; ; ; ; (, Transactions of the American Mathematical Society)
    Let K / Q p K/\mathbb {Q}_p be a finite unramified extension, ρ<#comment/> ¯<#comment/> : G a l ( Q ¯<#comment/> p / K ) →<#comment/> G L n ( F ¯<#comment/> p ) \overline {\rho }:\mathrm {Gal}(\overline {\mathbb {Q}}_p/K)\rightarrow \mathrm {GL}_n(\overline {\mathbb {F}}_p) a continuous representation, and τ<#comment/> \tau a tame inertial type of dimension n n . We explicitly determine, under mild regularity conditions on τ<#comment/> \tau , the potentially crystalline deformation ring R ρ<#comment/> ¯<#comment/> η<#comment/> , τ<#comment/> R^{\eta ,\tau }_{\overline {\rho }} in parallel Hodge–Tate weights η<#comment/> = ( n −<#comment/> 1 , ⋯<#comment/> , 1 , 0 ) \eta =(n-1,\cdots ,1,0) and inertial type τ<#comment/> \tau when theshapeof ρ<#comment/> ¯<#comment/> \overline {\rho } with respect to τ<#comment/> \tau has colength at most one. This has application to the modularity of a class of shadow weights in the weight part of Serre’s conjecture. Along the way we make unconditional the local-global compatibility results of Park and Qian [Mém. Soc. Math. Fr. (N.S.) 173 (2022), pp. vi+150]. 
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