arXiv subjects

Vijaykumar Singh

Publications and source records attributed to Vijaykumar Singh.

6 recordsLinked to original sources

arXiv2014

Generalized parity proofs of the Kochen-Specker theorem

We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed set of constraints and methods of linear algebra are used to produce subsets that are generalized parity proofs. Coding theory methods are used for enumeration of the proofs by size. In the second approach, one starts with the combinatorial structure of the set of constraints and one looks for ways to suitably populate this structure with observables. As well, we are able to show that many combinatorial structures can not produce parity proofs.

quant-ph↗

arXiv2011

Characteristic Polynomial of Supersingular Abelian Varieties over Finite Fields

In this article, we give a complete description of the characteristic polynomials of supersingular abelian varieties over finite fields. We list them for the dimensions upto 7.

math.AG↗

arXiv2011

The characteristic polynomials of abelian varieties of dimensions 4 over finite fields

We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite fields.

math.AG↗

arXiv2010

The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves

We study the intersection of two particular Fermat hypersurfaces in $\mathbb{P}^3$ over a finite field. Using the Kani-Rosen decomposition we study arithmetic properties of this curve in terms of its quotients. Explicit computation of the quotients is done using a Gröbner basis algorithm. We also study the $p$-rank, zeta function, and number of rational points, of the modulo $p$ reduction of the curve. We show that the Jacobian of the genus 2 quotient is $(4,4)$-split.

math.AG↗

arXiv2010

On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields

In this article, we derive a list of possible characteristic polynomials of the Frobenius of simple supersingular abelian varieties of dimension 1, 2, 3, 4, 5, 6, 7 over $\mathbb{F}_q$ where $q = p^n$, n odd.

math.AG↗

arXiv2010

On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields

In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ where $q=p^n$, $n$ odd.

math.AG↗