Related papers: Arithmetic level raising for certain quaternionic …

We establish an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on split toric varieties, for the height induced by any big and nef divisor class. This formula establishes new cases of the extension of Manin's…

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too…

Let $B/F$ be a quaternion algebra over a totally real number field. We give an explicit formula for heights of special points on the quaternionic Shimura variety associated with $B$ in terms of Faltings heights of CM abelian varieties.…

We give another proof of a theorem of H. Kajiura, K. Saito, and A. Takahashi based on the theory of weighted projective lines by Geigle and Lenzing and a theorem of Orlov on triangulated categories of graded B-branes. The content of this…

As a generalization of the Dedekind zeta function, Weng defined the high rank zeta functions and proved that they have standard properties of zeta functions, namely, meromorphic continuation, functional equation, and having only two simple…

We prove the Tate conjecture for integral degree 4 classes on a smooth cubic hypersurface X of dimension 4 over an algebraic closure of a field finitely generated over its prime subfield.

We prove a version of Ihara's Lemma for degree q=1,2 cuspidal cohomology of the symmetric space attached to automorphic forms of arbitrary weight (k\geq 2) over an imaginary quadratic field with torsion (prime power) coefficients. This…

Darmon points on p-adic tori and Jacobians of Shimura curves over Q were introduced in previous joint works with Rotger as generalizations of Darmon's Stark-Heegner points. In this article we study the algebraicity over extensions of a real…

We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli…

Let $A$ be a regular 2-dimensional local ring of characteristic $p>0$, and let $L/K$ be a cyclic extension of degree $p$ of its field of fractions such that the corresponding branch divisor is normal crossing. For each $\gp\in\Spec A$ of…

In the first part of the paper, we formulate several arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in the presence of ramification. The ramification comes from the choice of…

We construct the Bruhat--Tits stratification of the reduced locus of the ramified unitary Rapoport--Zink space of signature $(n-1,1)$, with the level being the stabilizer of a vertex lattice. We develop the local model theory for…

The classical Brauer-Siegel conjecture describes the asymptotic behaviour of the product of the class number and the regulator in families of number fields. All known cases of the conjecture rely on reducing the problem, via group theoretic…

We study the p-adic analogue of the arithmetic Gan-Gross-Prasad (GGP) conjectures for unitary groups. Let $\Pi$ be a conjugate-selfdual cuspidal automorphic representation of GL_{n} x GL_{n+1} over a CM field, which is algebraic of minimal…

In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic analogs of relative Langlands program. We explain related…

The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…

This paper is a continuation of our paper math.AG/0006222. We study the reduction of certain PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good"…

We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We use these results to prove many new cases…

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. In the…

This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a generic Riemann surface of genus at least four.