## Kodai Mathematical Journal

### Nilpotent admissible indigenous bundles via Cartier operators in characteristic three

Yuichiro Hoshi

#### Abstract

In the present paper, we study the p-adic Teichmüller theory in the case where p = 3. In particular, we discuss nilpotent admissible/ordinary indigenous bundles over a projective smooth curve in characteristic three. The main result of the present paper is a characterization of the supersingular divisors of nilpotent admissible/ordinary indigenous bundles in characteristic three by means of various Cartier operators. By means of this characterization, we prove that, for every nilpotent ordinary indigenous bundle over a projective smooth curve in characteristic three, there exists a connected finite étale covering of the curve on which the indigenous bundle is not ordinary. We also prove that every projective smooth curve of genus two in characteristic three is hyperbolically ordinary. These two applications yield negative, partial positive answers to basic questions in the p-adic Teichmüller theory, respectively.

#### Article information

Source
Kodai Math. J., Volume 38, Number 3 (2015), 690-731.

Dates
First available in Project Euclid: 30 October 2015

https://projecteuclid.org/euclid.kmj/1446210603

Digital Object Identifier
doi:10.2996/kmj/1446210603

Mathematical Reviews number (MathSciNet)
MR3417530

Zentralblatt MATH identifier
1349.14093

#### Citation

Hoshi, Yuichiro. Nilpotent admissible indigenous bundles via Cartier operators in characteristic three. Kodai Math. J. 38 (2015), no. 3, 690--731. doi:10.2996/kmj/1446210603. https://projecteuclid.org/euclid.kmj/1446210603