HPD-invariance of the Tate conjecture(s)

Notes on Tate Conjectures and Arakelov Theory

Remark 1.2. As a note on terminology, according to Milne, an affine variety over a field k is a variety isomorphic to the spectrum of a finitely generated k-algebra R such that R ⊗k k that has no nonzero nilpotents. A variety is a separated scheme admitting a covering by finitely many affine schemes [Mil, p. 5]. This is slightly different from Hartshorne’s definition; he requires the base field...

Tate Conjectures for Hilbert Modular Surfaces

On Beilinson’s Hodge and Tate Conjectures for Open Complete Intersections

In his lectures in [G1], M. Green gives a lucid explanation how fruitful the infinitesimal method in Hodge theory is in various aspects of algebraic geometry. A significant idea is to use Koszul cohomology for Hodge-theoretic computations. The idea originates from Griffiths work [Gri] where the Poincaré residue representation of the cohomology of a hypersurface played a crucial role in proving ...

A Remark on the Conjectures of Lang-trotter and Sato-tate on Average

We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves. Mathematics Subject Classification (2000): 11G05

Tautological Equations in M 3,1 via Invariance Conjectures

A new tautological equation of M3,1 in codimension 3 is derived and proved, using the invariance condition explained in [1, 9, 10, 11].