arXiv subjects

Harpreet Singh Bedi

Publications and source records attributed to Harpreet Singh Bedi.

3 recordsLinked to original sources

arXiv2020

Rational Degree Algebraic Geometry

Elementary Algebraic Geometry can be described as study of zeros of polynomials with integer degrees, this idea can be naturally carried over to `polynomials' with rational degree. This paper explores affine varieties, tangent space and projective space for such polynomials and notes the differences and similarities between rational and integer degrees. The line bundles $\mathcal{O}(n),n\in\mathbb{Q}$ are also constructed and their Čech cohomology computed.

math.GM↗

arXiv2019

Formal Schemes of Rational Degree

Non notherian Formal schemes of perfectoid type (for example $\mathbb{Z}_p[p^{1/p^\infty}]\langle X^{1/p^\infty} \rangle$ along with its multivariate version) with rational degree are constructed and are shown to be admissible. These formal schemes are a rational degree avatar of Tate affinoid algebras and come equipped with non Notherian rings. The corresponding notion of topologically finite presentation are defined and Gabber's Lemma, admissible blow ups (Raynaud's approach) are shown to hold under certain assumptions. A new notion of rings called eka$^d$ are introduced, which recover most examples of perfectoid affinoid algebras, without resorting to Huber's construction, Witt vectors or Frobenius. This version fixes some errors in the last version

math.AG↗

arXiv2017

Vector Bundles over Projectivoid Line

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

math.AG↗