F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)

The goal of this talk is to introduce a Gross--Zagier type formula, which relates the arithmetic self-intersection number of the Hodge bundle of a quaternionic Shimura curve over a totally real

Chavdarov and Zywina showed that after passing to a suitable field extension, every abelian surface A with real multiplication over some number field has geometrically simple reduction modulo p

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H

We show how to use the recent work of D. McKinnon and M. Roth on generalizations of Diophantine approximation to algebraic varieties to formulate a local version of the Batyrev-Manin principle on

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Sieves are an important tool in analytic number theory. In a typical sieve problem, one is given a list of p-adic conditions for all primes p, and the challenge is to count the number of integers

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour