2 results
Faltings height and Néron–Tate height of a theta divisor
- Part of
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 1 / January 2022
- Published online by Cambridge University Press:
- 24 January 2022, pp. 1-32
- Print publication:
- January 2022
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We prove a formula, which, given a principally polarized abelian variety
$(A,\lambda )$ over the field of algebraic numbers, relates the stable Faltings height of 
$A$ with the Néron–Tate height of a symmetric theta divisor on 
$A$. Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. The local non-archimedean terms in our formula can be expressed as the tropical moments of the tropicalizations of 
$(A,\lambda )$.
On the determinant bundles of abelian schemes
- Part of
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- Journal:
- Compositio Mathematica / Volume 144 / Issue 2 / March 2008
- Published online by Cambridge University Press:
- 01 March 2008, pp. 495-502
- Print publication:
- March 2008
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Let
be an abelian scheme over a scheme S which is quasi-projective over an affine noetherian scheme and let 
be a symmetric, rigidified, relatively ample line bundle on 
. We show that there is an isomorphism 
of line bundles on S, where d is the rank of the (locally free) sheaf 
. We also show that the numbers 24 and 12d are sharp in the following sense: if N>1 is a common divisor of 12 and 24, then there are data as above such that 
be an abelian scheme over a scheme 
be a symmetric, rigidified, relatively ample line bundle on 
. We show that there is an isomorphism 
. We also show that the numbers 24 and 12
