Related papers: Smith theory and cyclic base change functoriality

Let $X \overset{f}\longrightarrow S$ be a morphism of Noetherian schemes, with $S$ reduced. For any closed subscheme $Z$ of $X$ finite over $S$, let $j$ denote the open immersion $X\setminus Z \hookrightarrow X$. Koll\'ar asked whether for…

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T(n) be the telescope of a…

We study the action on the deformation space of a formal group by the maximal finite subgroup $G$ of its automorphisms, at the first height where the group has nontrivial $p$-torsion for odd $p$. We show given this group $G$ there is a…

We introduce and study the filtration on the space of automorphic functions (in the everywhere unramified situation for the function field case) obtained by transferring the filtration on the spectral side of the classical Langlands…

We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GL_n(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the…

We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…

We use the theory of trianguline $(\varphi,\Gamma)$-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at $p$, including those with characteristic $p$ coefficients.…

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the…

Fried's conjecture is concerned with the behavior of dynamical zeta functions at the origin. For compact hyperbolic manifolds, Fried proved that for an orthogonal acyclic representation of the fundamental group, the twisted Ruelle zeta…

In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

Let $\mathbf{G}$ be a reductive group and $\mathbf{X}$ a spherical $\mathbf{G}$-variety over a local non-archimedean field $\mathbb{F}$. We denote by $S(\mathbf{X}(\mathbb{F}))$ the Schwartz-functions on $\mathbf{X}(\mathbb{F})$. In this…

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…

We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of…

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation between…

We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and $\Delta$-complexes, respectively. The functors of classifying spaces and face posets are compatible with…

We review the Hodge theory of some classic examples from mirror symmetry, with an emphasis on what is intrinsic to the A-model, and on interesting open questions and problems. In particular, we illustrate the construction of a quantum…

According to the relative Langlands functoriality conjecture, an admissible morphism between the $L$-groups of spherical varieties should induce a functorial transfer of the corresponding local and global automorphic spectra. Via the…

Using an appropriate notion of locally convex Kasparov modules, we show how to induce isomorphisms under a large class of functors on the category of locally convex algebras; examples are obtained from spectral triples. Our considerations…