7 papers
Height Pairing on Higher Cycles and Mixed Hodge Structures II
J. I. Burgos Gil, S. Goswami, G. Pearlstein
To a pair of Bloch higher cycles that intersect properly and have complementary codimensions, we attach a mixed Hodge structure with some extra data (a framed mixed Hodge structure…
Pure extension of the theta divisor over the moduli space of abelian varieties
Ana MarÃa Botero, José Ignacio Burgos Gil, David Holmes +1
A theta divisor on the universal principally polarised abelian variety can be extended to a compactification either by taking the Zariski closure, or by taking the unique extension…
Closing the gap around the essential minimum of height functions with linear programming
José Burgos Gil, Ricardo Menares, Binggang Qu +1
For many common height functions, it is notoriously hard to compute the essential minimum. Nevertheless there are two classical methods, one giving lower bounds and the other givin…
A tropical formula for non-Archimedean local heights
José Ignacio Burgos Gil, Walter Gubler, Klaus Künnemann
We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for . These delta-forms will be used to define the star-product with Green funct…
On the height of the universal abelian variety
José Ignacio Burgos Gil, Jürg Kramer
In this paper we extend the arithmetic intersection theory of adelic divisors on quasiprojective varieties developed by X. Yuan and S. W. Zhang to cover certain adelic arithmetic d…
Tempered currents and Deligne cohomology of Shimura varieties, with an application to
José Ignacio Burgos Gil, Antonio Cauchi, Francesco Lemma +1
We provide a new description of Deligne-Beilinson cohomology for any Shimura variety in terms of tempered currents. This is particularly useful for computations of regulators of mo…