Descent theory of simple sheaves on $C_1$-fields

Ananyo Dan; Inder Kaur

doi:10.21711/231766362020/rmc474

Descent theory of simple sheaves on $C_1$-fields

Algebraic Geometry 2022-04-19 v1

Authors: Ananyo Dan , Inder Kaur

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Let $K$ be a $C_1$ -field of any characteristic and $X$ a projective variety over $K$ . In this article we prove that for a finite Galois extension $L$ of $K$ , a simple sheaf with covering datum on $X \times_K L$ descends to a simple sheaf on $X$ . As a consequence, we show that there is a $1-1$ correspondence between the set of geometrically stable sheaves on $X$ with fixed Hibert polynomial $P$ and the set of $K$ -rational points of the corresponding moduli space.

Keywords

c1-field simple sheaf descent theory galois extension projective variety moduli space geometrically stable sheaf

Cite

@article{arxiv.2204.08075,
  title  = {Descent theory of simple sheaves on $C_1$-fields},
  author = {Ananyo Dan and Inder Kaur},
  journal= {arXiv preprint arXiv:2204.08075},
  year   = {2022}
}

Comments

Appeared in the Proceedings of the ICM 2018 satellite 'Moduli spaces in Algebraic Geometry and Applications'

Descent theory of simple sheaves on $C_1$-fields

Abstract

Keywords

Cite

Comments

Related papers