Let A be a separable (not necessarily unital) simple -algebra with strict comparison. We show that if A has tracial approximate oscillation zero, then A has stable rank one and the canonical map from the Cuntz semigroup of A to the corresponding lower…
In this paper, we investigate the theory of heights in a family of stacky curves following recent work of Ellenberg, Satriano, and Zureick-Brown. We first give an elementary construction of a height which is seen to be dual to theirs. We count rational…
We prove a weak version of the cross-product conjecture: , where is the number of linear extensions for which the values at fixed elements are k and apart, respectively, and where depends on the poset. We also prove the converse inequality and disp…
We continue our study from Peterzil et al. (2022, Preprint, arXiv:2208.08293) of finite-dimensional definable groups in models of the theory , the model companion of an o-minimal -theory T expanded by a generic derivation as in Fornasiero and Kaplan (…
To understand the p-adic étale cohomology of a proper smooth variety over a p-adic field, Faltings compared it to the cohomology of his ringed topos, by the so-called Faltings’ main p-adic comparison theorem, and then deduced various comparisons with p…
This paper goes beyond Katz–Sarnak theory on the distribution of curves over finite fields according to their number of rational points, theoretically, experimentally, and conjecturally. In particular, we give a formula for the limits of the moments me…
The notion of indicator of an analytic function, that describes the function’s growth along rays, was introduced by Phragmen and Lindelöf. Trigonometric convexity is a defining property of the indicator. For multivariate cases, an analogous property of…
In this paper, we study the Dirichlet problem for systems of mean value equations on a regular tree. We deal both with the directed case (the equations verified by the components of the system at a node in the tree only involve values of the unknowns a…