## Kodai Mathematical Journal

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

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

#### 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

**Permanent link to this document**

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