Using arithmetic intersection theory, a theory of heights for projective varieties over rings of
algebraic integers is developed. These heights are generalizations of those considered by …

Arakelov theory is a new geometric approach to diophantine equations. It combines
algebraic geometry, in the sense of Grothendieck, with refined analytic tools such as …

Consider following generalized Bogomolov conjecture: Let A be an abelian variety over Q,
h: A (Q)→ R a Néron-Tate height function with respect to an ample and symmetric line …

For an arithmetic variety and a positive hermitian line bundle, in this paper, we compute the
leading term of the Hilbert function of the line bundle, show the ampleness of the line …

Mesures et équidistribution sur les espaces de Berkovich Page 1 J. reine angew. Math. 595
(2006), 215—235 DOI 10.1515/CRELLE.2006.049 Journal für die reine und angewandte …

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real
fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series …

Let i: Y—> X be an embedding of compact complex manifolds. Let r| be a holomorphic vector
bundle on Y and let (0.1)(^): o^-^ _,...-^-. 0 vv be a holomorphic chain complex of vector …

We prove in this paper an arithmetic analog of the Riemann-Roch-Grothendieck theorem for
the determinant of the cohomology of an Hermitian vector bundle of arbitrary rank on a …

Soient K un corps de nombres et K sa cloture algebrique. Soient XK une courbe propre,
lisse, geometriquement connexe de genre g> 2 sur K et J sa jacobienne. Soit Do un diviseur …

Siegel's Theorem in the Compact Case Page 1 Annals of Mathematics, 133 (1991), 509-548
Siegel's theorem in the compact case By PAUL VOJTA* This paper gives a proof of Mordell's …