Curvature on the integers, II

TL;DR

This paper introduces a new concept of curvature on integers using algebraic methods, providing key theorems on its behavior for classical groups' Chern connections, expanding the mathematical understanding of integer curvature.

Contribution

It presents an alternative notion of curvature on integers based on algebraization of Frobenius lifts, independent of prior analytic continuation approaches.

Findings

Vanishing theorems for certain curvature cases

Non-vanishing results for specific classical groups

Enhanced understanding of integer curvature in algebraic geometry

Abstract

In a prequel to this paper \cite{curvature1} a notion of curvature on the integers was introduced, based on the technique of "analytic continuation between primes", introduced in \cite{laplace}. In this paper, which is essentially independent of its prequel, we introduce another notion of curvature on the integers, based on "algebraization of Frobenius lifts by correspondences." Our main results are vanishing/non-vanishing theorems for this new type of curvature in the case of "Chern connections" attached to classical groups.