Let $K$ be a field of prime characteristic $p$, $n>4 $ an integer, $f(x)$ irreducible polynomial over degree $n$, whose Galois group is either the full symmetric $S_n$ or alternating $A_n$. $l$ odd different from $Z[\zeta_l]$ ring integers in $l$th cyclotomic field, $C_{f,l}:y^l=f(x)$ corresponding superelliptic curve and $J(C_{f,l})$ its jacobian. We prove that all endomorphisms coincides with...

The classical Poincar\'e formula relates the rational homology classes of tautological cycles on a Jacobian to powers class Riemann theta divisor. We prove tropical analogue this formula. Along way, we several foundational results about real tori with integral structures (and, therefore, abelian varieties). For example, version Appell-Humbert theorem. also study various notions equivalences bet...

Abstract Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant each is moment. We give an explicit and efficiently computable formula for the moment of Jacobian in terms potential theory on underlying graph. show that there exists universal linear relation between moment, certain capacity tau invariant, total ...