ﻻ يوجد ملخص باللغة العربية
Let $p$ be a prime number. We prove that the $P=W$ conjecture for $mathrm{SL}_p$ is equivalent to the $P=W$ conjecture for $mathrm{GL}_p$. As a consequence, we verify the $P=W$ conjecture for genus 2 and $mathrm{SL}_p$. For the proof, we compute the perverse filtration and the weight filtration for the variant cohomology associated with the $mathrm{SL}_p$-Hitchin moduli space and the $mathrm{SL}_p$-twisted character variety, relying on Grochenig-Wyss-Zieglers recent proof of the topological mirror conjecture by Hausel-Thaddeus. Finally we discuss obstructions of studying the cohomology of the $mathrm{SL}_n$-Hitchin moduli space via compact hyper-Kahler manifolds.
We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus $2$ curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holds for the subalgebra of cohomology generated by even
We explore the cohomological structure for the (possibly singular) moduli of $mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the $mathrm{SL}_n$-
Let $E/F$ be a quadratic extension of number fields and let $pi$ be an $mathrm{SL}_n(mathbb{A}_F)$-distinguished cuspidal automorphic representation of $mathrm{SL}_n(mathbb{A}_E)$. Using an unfolding argument, we prove that an element of the $mathrm{
Let $p$ be a prime number and $K$ a finite extension of $mathbb{Q}_p$. We state conjectures on the smooth representations of $mathrm{GL}_n(K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular, when $K$ is
Let $L$ be a finite extension of $mathbb{Q}_p$, and $rho_L$ be an $n$-dimensional semi-stable non crystalline $p$-adic representation of $mathrm{Gal}_L$ with full monodromy rank. Via a study of Breuils (simple) $mathcal{L}$-invariants, we attach to $