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تسجيل مستخدم جديدCompanion points and locally analytic socle for $mathrm{GL}_2(L)$
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تأليف
Yiwen Ding
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Let $p>2$ be a prime number, and $L$ be a finite extension of $mathbb{Q}_p$, we prove Breuils locally analytic socle conjecture for $mathrm{GL}_2(L)$, showing the existence of all the companion points on the definite (patched) eigenvariety. This work relies on infinitesimal R=T results for the patched eigenvariety and the comparison of (partially) de Rham families and (partially) Hodge-Tate families. This method allows in particular to find companion points of non-classical points.
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We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuils locally analytic socle conjecture for $mathrm{GL}_n(mathbb{Q}_p)$.
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Let $rho_p$ be a $3$-dimensional $p$-adic semi-stable representation of $mathrm{Gal}(overline{mathbb{Q}_p}/mathbb{Q}_p)$ with Hodge-Tate weights $(0,1,2)$ (up to shift) and such that $N^2 e 0$ on $D_{mathrm{st}}(rho_p)$. When $rho_p$ comes from an au
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Let $F$ be a totally real number field, $wp$ a place of $F$ above $p$. Let $rho$ be a $2$-dimensional $p$-adic representation of $mathrm{Gal}(bar{F}/F)$ which appears in the etale cohomology of quaternion Shimura curves (thus $rho$ is associated to H
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