A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship bet...

In this paper, we will consider an arithmetic analogue of relative Bogomolov's inequality in [14]. We also establish arithmetic Riemann-Roch formulae for stable curves over regular arithmetic varieties and generically nite morphisms of arithmetic varieties.