Automorphism Groups on Tropical Curves: Some Cohomology Calculations

Abstract

Let $X$ be an abstract tropical curve and let $G$ be a finite subgroup of the automorphism group of $X$. Let $D$ be a divisor on $X$ whose equivalence class is $G$-invariant. We address the following question: is there always a divisor $D^{\prime }$ in the equivalence class of $D$ which is $G$-invariant? Our main result is that the answer is "yes" for all abstract tropical curves. A key step in our proof is a tropical analogue of Hilbert's Theorem 90.

17 pages. Comments welcome. Version 2: plugged a small leak in the proof of Prop.1, section 5; fixed typos and added an acknowledgement

References in corpus (1)

• A primer on computational group homology and cohomology