Séminaire de Géométrie Tropicale
Mercredi 22 mai, 16h15 salle 1525-502
Balancing conditions in global tropical geometry
Résumé :
We study tropical geometry in the global setting using the deformation retraction of a non-Archimedean analytic space to its skeleton constructed by V. Berkovich. We state and prove the generalized balancing conditions in this setting. Starting with a strictly stable formal scheme, we calculate certain sheaves of vanishing cycles using analytic étale cohomology, then interpret tropical weights by these cycles. We obtain the balancing condition for tropical curves on the skeleton associated to the formal scheme in terms of the intersection theory on the special fibre. Our approach works over any complete discrete valuation field.