Total p-differentials on schemes over Z/p2

被引：5

作者：

Dupuy, Taylor ^{[1
]}

Katz, Eric ^{[2
]}

Rabinoff, Joseph ^{[3
]}

Zureick-Brown, David ^{[4
]}

机构：

[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05405 USA

[2] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

[3] Georgia Inst Technol, Sch Math, 686 Cherry St, Atlanta, GA 30332 USA

[4] Emory Univ, Dept Math & CS, 400 Dowman Dr,W401, Atlanta, GA 30322 USA

来源：

JOURNAL OF ALGEBRA | 2019年 / 524卷

基金：

欧洲研究理事会;

关键词：

Witt vectors; Algebraic geometry over finite fields; Frobenius lifts; Arithmetic differential equations;

D O I：

10.1016/j.jalgebra.2019.01.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a scheme X defined over the length 2 p-typical Witt vectors W-2(k) of a characteristic p field, we introduce total p-differentials which interpolate between Frobenius-twisted differentials and Buium's p-differentials. They form a sheaf over the reduction X-0, and behave as if they were the sheaf of differentials of X over a deeper base below W-2(k). This allows us to construct the analogues of Gauss-Manin connections and Kodaira Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weiland's biring formalism, and Deligne-Illusie classes. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：110 / 123

页数：14

共 13 条

[1] Plethystic algebra [J].

Borger, J ;

Wieland, B .

ADVANCES IN MATHEMATICS, 2005, 194 (02) :246-283

[2]

Borger J, 2009, ARXIV09063146

[3] Arithmetic analogues of derivations [J].

Buium, A .

JOURNAL OF ALGEBRA, 1997, 198 (01) :290-299

[4] DIFFERENTIAL CHARACTERS OF ABELIAN-VARIETIES OVER P-ADIC FIELDS [J].

BUIUM, A .

INVENTIONES MATHEMATICAE, 1995, 122 (02) :309-340

[5] Geometry of p-jets [J].

Buium, A .

DUKE MATHEMATICAL JOURNAL, 1996, 82 (02) :349-367

[6]

Buium A, 2005, ARITHMETIC DIFFERENT, V118

[7] P2 MODULES AND DECOMPOSITION OF THE DERHAM COMPLEX [J].

DELIGNE, P ;

ILLUSIE, L .

INVENTIONES MATHEMATICAE, 1987, 89 (02) :247-270

[8]

Dupuy Taylor, PREPRINT

[9]

Dupuy Taylor, 2018, ARXIV180400228

[10]

Dupuy Taylor, 2017, ARXIV170708714

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