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Examples of abelian surfaces with non-square Tate-Shafarevich group
Examples of abelian surfaces non-square Tate-Shafarevich group Number Theory
2012/6/30
In this article we show the existence of abelian surfaces over Q with Tate-Shafarevich groups having orders five times a square and seven times a square. To obtain this result, we explore the invarian...
Quadratic congruences on average and rational points on cubic surfaces
Quadratic congruences rational points Manin’s conjecture cubic surfaces universal torsors
2012/5/24
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
Geodesic restrictions of eigenfunctions on arithmetic surfaces
Geodesic restrictions of eigenfunctions arithmetic surfaces Number Theory
2012/4/23
Let X be an arithmetic hyperbolic surface, {\psi} a Hecke-Maass form, and {\gamma} a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of ...
Intersection theory on Shimura surfaces II
Intersection theory Shimura surfaces II Number Theory
2012/3/1
This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed t...
Intersection theory on Shimura surfaces
Intersection theory Shimura surfaces intersection multiplicities
2012/3/1
Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, ...
Algebraic density property of Danilov-Gizatullin surfaces
Algebraic density property Danilov-Gizatullin surfaces
2010/12/9
A Danilov-Gizatullin surface is an affine surface V which is the com-plement of an ample section S of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism...
A correspondence between various Pin-type structures on a compact surface and quadratic (Iinear) forms on its homology is constructed. Sum of structures is defined and expressed in terms of these quad...