On bt1 group schemes and fermat curves

Rachel Pries; Douglas Ulmer

On bt₁ group schemes and fermat curves

Rachel Pries
, Douglas Ulmer

Research output: Contribution to journal › Article › peer-review

Abstract

Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT₁ group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. We compare three classifications of BT₁ group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl–Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.

Original language	English (US)
Pages (from-to)	705-739
Number of pages	35
Journal	New York Journal of Mathematics
Volume	27
State	Published - 2021
Externally published	Yes

Keywords

Abelian variety
Curve
De rham cohomology
Dieudonné module
Ekedahl–oort type
Fermat curve
Finite field
Frobenius
Group scheme
Jacobian
Verschiebung

ASJC Scopus subject areas

General Mathematics

Cite this

@article{dec9769ec86f44df82dce87591cf3868,

title = "On bt1 group schemes and fermat curves",

abstract = "Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT1 group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. We compare three classifications of BT1 group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl–Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.",

keywords = "Abelian variety, Curve, De rham cohomology, Dieudonn{\'e} module, Ekedahl–oort type, Fermat curve, Finite field, Frobenius, Group scheme, Jacobian, Verschiebung",

author = "Rachel Pries and Douglas Ulmer",

note = "Funding Information: DMS-1901819, and author DU was partially supported by Simons Foundation grants 359573 and 713699. We would like to thank the referee for a thoughtful and very fast report. Funding Information: Acknowledgements. Author RP was partially supported by NSF grant Publisher Copyright: {\textcopyright} 2021, University at Albany. All rights reserved.",

year = "2021",

language = "English (US)",

volume = "27",

pages = "705--739",

journal = "New York Journal of Mathematics",

issn = "1076-9803",

publisher = "University at Albany",

}

TY - JOUR

T1 - On bt1 group schemes and fermat curves

AU - Pries, Rachel

AU - Ulmer, Douglas

N1 - Funding Information: DMS-1901819, and author DU was partially supported by Simons Foundation grants 359573 and 713699. We would like to thank the referee for a thoughtful and very fast report. Funding Information: Acknowledgements. Author RP was partially supported by NSF grant Publisher Copyright: © 2021, University at Albany. All rights reserved.

PY - 2021

Y1 - 2021

N2 - Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT1 group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. We compare three classifications of BT1 group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl–Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.

AB - Let p be a prime number and let k be an algebraically closed field of characteristic p. A BT1 group scheme over k is a finite commutative group scheme which arises as the kernel of p on a p-divisible (Barsotti–Tate) group. We compare three classifications of BT1 group schemes, due in large part to Kraft, Ekedahl, and Oort, and defined using words, canonical filtrations, and permutations. Using this comparison, we determine the Ekedahl–Oort types of Fermat quotient curves and we compute four invariants of the p-torsion group schemes of these curves.

KW - Abelian variety

KW - Curve

KW - De rham cohomology

KW - Dieudonné module

KW - Ekedahl–oort type

KW - Fermat curve

KW - Finite field

KW - Frobenius

KW - Group scheme

KW - Jacobian

KW - Verschiebung

UR - https://www.scopus.com/pages/publications/85116229669

UR - https://www.scopus.com/pages/publications/85116229669#tab=citedBy

M3 - Article

AN - SCOPUS:85116229669

SN - 1076-9803

VL - 27

SP - 705

EP - 739

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

On bt₁ group schemes and fermat curves

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this