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arXiv · 2204.08075

Descent theory of simple sheaves on $C_1$-fields

Ananyo Dan·Inder Kaur
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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.

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Ananyo Dan, Inder Kaur. 2022-04-17. Descent theory of simple sheaves on $C_1$-fields. https://doi.org/10.21711/231766362020/rmc474

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