What question did this study set out to answer?

This research aims to establish conditions under which certain differential forms are residue free on n-dimensional algebraic schemes.

April 4, 2026Open Access

ON RESIDUE FREE DIFFERENTIAL FORMS OF AN ALGEBRAIC SCHEME OVER A FIELD OF CHARACTERISTIC p

Key Points

This research aims to establish conditions under which certain differential forms are residue free on n-dimensional algebraic schemes.
Consider non-singular algebraic integral schemes over perfect fields of characteristic p.
Analyze differential forms in the context of algebraic function fields.
Demonstrate the equivalence of three specific conditions related to residue free status.
Identified three equivalent conditions that characterize residue free differential forms.
Generalized a theorem from Nakakoshi regarding the degree of differential forms.

Abstract

Let V be an n-dimensional non-singular algebraic integral scheme over a perfect field k of characteristic p > 0 and K its algebraic function field.In this paper, we will prove the following:Let be a differential form in Z (K/k).Then the following three conditions are equivalent:(1) is residue free on V , (2) there exists an integer N such thatThe above theorem is a generalization of the main theorem in Nakakoshi 5.He proved the theorem in case of degree() = n.

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