Related papers: Godement--Jacquet L-function and homological theta…
The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…
We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic integration, we show that the zeta functions associated to…
We consider a functional analytic variant of the notion of Tate space, namely the category of those topological vector spaces which have a direct sum decomposition where one summand is nuclear Frechet space and the other is the dual of a…
We propose a motivic version of T. Hausel and M. Thaddeus' Topological Mirror Symmetry for character stacks associated with arbitrary semisimple groups, which is an analogue of F. Loeser and D. Wyss' result for Chow motives of moduli spaces…
The Kawazumi-Zhang invariant $\varphi$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known…
We give new instances where Chabauty--Kim sets can be proved to be finite, by developing a notion of "generalised height functions" on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals…
We prove two conjectures regarding the representation growth of groups of type $A_2$. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation…
By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As applications, we establish two hyperbolicity-related results.…
We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a…
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the…
We define geometric zeta functions for locally symmetric spaces as generalizations of the zeta functions of Ruelle and Selberg. As a special value at zero we obtain the Reidemeister torsion of the manifold. For hermitian spaces these zeta…
We give a new and representation theoretic construction of $p$-adic interpolation series for central values of self-dual Rankin-Selberg $L$-functions for $\operatorname{GL}_2$ in dihedral towers of CM fields, using expressions of these…
We define a regularized theta lift from SL_2 to orthogonal groups over totally real fields. It takes harmonic `Whittaker forms' to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal…
We prove that a cuspidal automorphic representation of GL(3) over any number field is determined by the quadratic twists of its central value. In the case of a non-Gelbart-Jacquet lift, the result is conditional on the analytic behavior of…
In this paper, we study Fontaine-Laffaille, self-dual deformations of a mod p non-semisimple Galois representation of dimension n with its Jordan-Holder factors being three mutually non-isomorphic absolutely irreducible representations. We…
We embed the Lubin-Tate tower into a larger tower of formal schemes, the "degenerating Lubin-Tate tower." We construct a topological realization of the degenerating Lubin-Tate tower, i.e., a compatible family of presheaves of…
We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. We utilize -- and reprove -- D. Anick's fundamental result on…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…
In Part I of the present series of papers, we adumbrate our idea of Riemannian geometry to higher order in the infinitesimals and derive expressions for the appropriate generalizations of parallel transport and the Riemannian curvature…
Howe and Tan (1993) investigated a degenerate principal series representation of indefinite orthogonal groups $\mathrm{O}(V)$ and explicitly described its composition series. They showed that there exists a unique unitarizable irreducible…