Blueprints and Tropical Scheme Theory

In this lecture, we will introduce blueprints and blue schemes and explain how this theory can be used to endow the tropicalization of a classical variety with a schematic structure.
Once the basic constructions are explained, we discuss balancing conditions and conncetions to related theories as skeleta of Berkovich spaces, toroidal embeddings and log-structures. We put a particular weight on explaining open problems in this very young branch of tropical geometry.

Prerequisites: Basic knowledge of scheme theory, e.g. Hartshorne, Chapter 2.

The times for this course will be discussed during the first meeting on Monday, March 12, at 13:30, in room 228.
http://w3.impa.br/~lorschei/2018-Blueprints/blueprints.html

References:
Jeffrey Giansiracusa and Noah Giansiracusa. Equations for tropical varieties. Duke Math. J., 165(18):3379-3433, 2016.
Jeffrey Giansiracusa and Noah Giansiracusa. The universal tropicalization and the Berkovich analytification. Preprint, arXiv:1410.4348, 2014.
Oliver Lorscheid. Scheme theoretic tropicalization. Preprint, arXiv:1508.07949, 2015.
Diane Maclagan and Felipe Rincon. Tropical schemes, tropical cycles, and valuated matroids. Preprint, arXiv:1401.4654, 2014.
Diane Maclagan and Felipe Rincon. Tropical ideals. Preprint, arXiv:1609.03838, 2016.

* Standard program. The teacher has the autonomy to make any changes