In this paper we give a geometric description of the behavior of analytic intertwining operators between parabolically induced representations of $\mathrm{GL}_n(\mathrm{F})$, where $\mathrm{F}$ is a local non-archimedean field, in terms of hyperbolic localization functors of Braden. As a consequence, we can show that the image of an intertwining operator is always semi-simple and give a lower bound on the order of its pole, which is conjectured to be an equality as well as an upper bound in terms of the singular support of certain perverse sheaves. Moreover, we are able to reduce the conjecture of Lapid and M\'inguez on the shape of irreducible subrepresentations of induced representations to a computation of characteristic cycles. The theory of mixed Hodge modules plays a crucial role in the proofs.
We develop a framework for studying discrete subgroups of $\mathsf{PGL}(d+1,\mathbb{R})$ via the paracomplex hyperbolic space $\mathbb{H}_\tau^d$, a rank-$1$ pseudo-Riemannian symmetric space. We characterize projective transverse, relatively Anosov, and Anosov subgroups in terms of properly discontinuous, geometricall...
We establish an Arakelov inequality for variations of Hodge structures underlying families of principally polarized complex Abelian varieties. In the equality case, this leads to a numerical characterization of certain totally geodesic ball quotients inside the moduli space of Abelian varieties. Our result extends work...
Matteo Costantini, D. Greb, C. Tamborini· 0 citations
We study the $\mathbf{I}^*$-cohomology of a smooth real algebraic curve in terms of its real locus and its geometric genus. We notably extend results of Monnier to the twisted case, which is crucial to the understanding of proper pushforwards of Witt groups. We also perform some computations related to transfers along...
In this paper, we extend a large part of the uniformization theory of Bonk-Heinonen-Koskela [Asterisque 2001] to length spaces that are not necessarily proper or geodesic. Among other things, we show that there is a one-to-one correspondence between the quasiisometry classes of complete roughly starlike Gromov hyperbol...
The key part of the current paper is the computation of boundary and Eisenstein cohomology of $GL_4({\mathbb Z})$ with coefficient in any highest weight representations. The method we develop let us compute in an alternative way the cohomology of $SL_3({\mathbb Z})$ and of $GL_3({\mathbb Z})$ with coefficients in any h...
Let $\mathscr{O}_K$ be a mixed characteristic complete DVR with perfect residue field $k$, and let $\mathfrak{X}$ be a proper formal scheme over $\mathscr{O}_K$ with semistable reduction. Answering a question of Fontaine and Jannsen, a classical theorem of Hyodo and Kato gives a rational identification between the log...
F. Binda, S. Saito· 0 citations
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