Matroids with coefficients and F₁-geometry

Manoel Zanoelo Jarra's thesis is divided into two parts. The first one is devoted to geometry over the so-called field with one element. In particular, Zanoelo Jarra introduces a concept of dimension for F1-schemes and a natural framework for presenting a possible approach to the ABC conjecture.

In the second part Zanoelo Jarra adds the following new building blocks to the theory of matroids with coefficients: a description of matroids in terms of exterior algebras; morphisms of matroids; flag matroids and quiver matroids. Moreover, he studied moduli spaces of (flags and quiver) matroids and investigated the relation between their F1-rational points and Euler characteristics of complex quiver Grassmannians.

Dissertation: https://hdl.handle.net/11370/3f4719ba-a1f2-492a-86dd-ec52d8112a3a