Tohoku Mathematical Journal
2021
December
SECOND SERIES VOL. 73, NO. 4

Tohoku Math. J.
73 (2021), 471-538

Title INVARIANTS OF ALGEBRAIC VARIETIES OVER IMPERFECT FIELDS

Author Hiromu Tanaka

(Received May 7, 2019, revised June 1, 2020)
Abstract. We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of these invariants. We then apply our results to curves over imperfect fields. In particular, we establish a genus change formula and prove the boundedness of non-smooth regular curves of genus one. We also compute our invariants for some explicit examples.

Mathematics Subject Classification. Primary 14G17; Secondary 14D06.
Key words and phrases. Imperfect fields, generic fibres, positive characteristic.

To the top of this page

Back to the Contents