Divisorial fans and algebraic torus actions over arbitrary fields

Abstract

We provide an algebro-geometric combinatorial description of normal varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of divisorial fans endowed with a Galois semilinear action. This work concludes the description of normal $T$-varieties over fields.

arXiv comment57 pages. Comments are welcome:). Improvements on the readability. Some results were took off and the sections have been reorganized. Corrections of Lemma 2.2 and Proposition 3.10 have been made