arXiv subjects
Publications and source records attributed to Arjun Nigam.
We compute the $2$-completed integral motivic homology, effective algebraic K-theory, and very effective hermitian K-theory of the geometric classifying space of the cyclic group of order two over algebraically closed fields, the real numbers, and finite fields.
In this paper, we examine certain maximal rank sublattices of the Mordell-Weil lattices of two families of elliptic curves over fields of characteristic $p > 0$. We compute explicit lower bounds on the densest sphere packings of these sublattices by finding lower bounds on the minimal norms of the sublattices and explicitly computing the volumes of their fundamental domains.
In this paper, we define a $k$-Diophantine $m$-tuple to be a set of $m$ positive integers such that the product of any $k$ distinct positive integers is one less than a perfect square. We study these sets in finite fields $\mathbb{F}_p$ for odd prime $p$ and guarantee the existence of a $k$-Diophantine m-tuple provided $p$ is larger than some explicit lower bound. We also give a formula for the number of 3-Diophantine triples in $\mathbb{F}_p$ as well as an asymptotic formula for the number of $k$-Diophantine $k$-tuples.
This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this subalgebra due to Reiner and Tudose. The first reinterprets it in terms of the operation of $k$-conjugation, suggesting two conjectural bases for the subalgebras that would imply their conjecture. The second introduces an analogous conjecture for the cohomology of Lagrangian Grassmannians.