6 papers
On -adic solubility of
Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin
We study -adic solubility of generalized Fermat equations for positive integers . For all but finitely many primes , the probability of…
The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations
Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin +3
We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus that are defined using generalized Fermat equations, extend…
Wild Stacky Curves and Rings of Mod p Modular Forms
Andrew Kobin, David Zureick-Brown
We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic , which allows us to compute rings of…
Artin-Schreier-Witt Theory for Stacky Curves
Andrew Kobin
We extend our previous classification of stacky curves in positive characteristic using higher ramification data and Artin-Schreier-Witt theory. The main new technical tool introdu…
Arithmetic Functions and Geometry
Andrew Kobin
In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's -function - within a unif…
Categorifying Zeta Functions for Quadratic Covers
Jon Aycock, Andrew Kobin
In various contexts, the zeta function of an object splits into a product of -functions. We categorify this product formula for quadratic covers of objects in the following cont…