Rigid-analytic varieties with projective reduction violating Hodge symmetry

被引：2

作者：

Petrov, Alexander ^{[1
]}

机构：

[1] Harvard Univ, Dept Math, 1 Oxford St, Cambridge, MA 02138 USA

来源：

COMPOSITIO MATHEMATICA | 2021年 / 157卷 / 03期

关键词：

rigid-analytic varieties; Hodge symmetry; p-adic Hodge theory;

D O I：

10.1112/S0010437X20007708

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct examples of smooth proper rigid-analytic varieties admitting formal models with projective special fibers and violating Hodge symmetry for cohomology in degrees >= 3. This answers negatively the question raised by Hansen and Li.

引用

页码：625 / 640

页数：17

共 50 条

[1] p-ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES
Scholze, Peter
[J]. FORUM OF MATHEMATICS PI, 2013, 1
[2] On rigid-analytic Picard varieties
Hartl, U
Lütkebohmert, W
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2000, 528 : 101 - 148
[3] Rigid-analytic geometry and the uniformization of abelian varieties
Papikian, M
[J]. SNOWBIRD LECTURES IN ALGEBRAIC GEOMETRY, 2005, 388 : 145 - 160
[4] p-ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES (vol 1, e1, 2013)
Scholze, Peter
[J]. FORUM OF MATHEMATICS PI, 2016, 4
[5] Line bundles on rigid varieties and Hodge symmetry
David Hansen
Shizhang Li
[J]. Mathematische Zeitschrift, 2020, 296 : 1777 - 1786
[6] Line bundles on rigid varieties and Hodge symmetry
Hansen, David
Li, Shizhang
[J]. MATHEMATISCHE ZEITSCHRIFT, 2020, 296 (3-4) : 1777 - 1786
[7] ON RIGID VARIETIES WITH PROJECTIVE REDUCTION
Li, Shizhang
[J]. JOURNAL OF ALGEBRAIC GEOMETRY, 2020, 29 (04) : 669 - 690
[8] RIGID-ANALYTIC L - TRANSFORMS
SCHNEIDER, P
[J]. LECTURE NOTES IN MATHEMATICS, 1984, 1068 : 216 - 230
[9] Hodge symmetry for rigid varieties via log hard Lefschetz
Achinger, Piotr
[J]. MATHEMATICAL RESEARCH LETTERS, 2023, 30 (01) : 1 - 31
[10] Deformation theory of rigid-analytic spaces
Iwanar, Isamu
[J]. JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2007, 47 (04): : 691 - 715

← 1 2 3 4 5 →