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We compute the etale cohomology ring $H^*(text{Spec } mathcal{O}_K,mathbb{Z}/nmathbb{Z})$ where $mathcal{O}_K$ is the ring of integers of a number field $K.$ As an application, we give a non-vanishing formula for an invariant defined by Minhyong Kim.
We present a variation of the modular algorithm for computing the Hermite normal form of an $mathcal O_K$-module presented by Cohen, where $mathcal O_K$ is the ring of integers of a number field $K$. An approach presented in (Cohen 1996) based on red
For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgroup
One of the many number theoretic topics investigated by the ancient Greeks was perfect numbers, which are positive integers equal to the sum of their proper positive integral divisors. Mathematicians from Euclid to Euler investigated these mysterious
Most hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by the appropriat
We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-equivariant sheaf of graded algebras on X whose G-invariant global secti