---
_id: '9099'
abstract:
- lang: eng
text: We show that on an Abelian variety over an algebraically closed field of positive
characteristic, the obstruction to lifting an automorphism to a field of characteristic
zero as a morphism vanishes if and only if it vanishes for lifting it as a derived
autoequivalence. We also compare the deformation space of these two types of deformations.
acknowledgement: I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina
Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas
Hausel for hosting me in his research group at IST Austria, and the referees for
their valuable suggestions. This research has received funding from the European
Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie
Grant Agreement No. 754411.
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. Lifting automorphisms on Abelian varieties as derived autoequivalences.
Archiv der Mathematik. 2021;116(5):515-527. doi:10.1007/s00013-020-01564-y
apa: Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived
autoequivalences. Archiv Der Mathematik. Springer Nature. https://doi.org/10.1007/s00013-020-01564-y
chicago: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
Autoequivalences.” Archiv Der Mathematik. Springer Nature, 2021. https://doi.org/10.1007/s00013-020-01564-y.
ieee: T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,”
Archiv der Mathematik, vol. 116, no. 5. Springer Nature, pp. 515–527, 2021.
ista: Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived
autoequivalences. Archiv der Mathematik. 116(5), 515–527.
mla: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
Autoequivalences.” Archiv Der Mathematik, vol. 116, no. 5, Springer Nature,
2021, pp. 515–27, doi:10.1007/s00013-020-01564-y.
short: T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527.
date_created: 2021-02-07T23:01:13Z
date_published: 2021-05-01T00:00:00Z
date_updated: 2023-08-07T13:42:38Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00013-020-01564-y
ec_funded: 1
external_id:
arxiv:
- '2001.07762'
isi:
- '000612580200001'
intvolume: ' 116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.07762
month: '05'
oa: 1
oa_version: Preprint
page: 515-527
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Archiv der Mathematik
publication_identifier:
eissn:
- '14208938'
issn:
- 0003889X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lifting automorphisms on Abelian varieties as derived autoequivalences
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 116
year: '2021'
...
---
_id: '9173'
abstract:
- lang: eng
text: We show that Hilbert schemes of points on supersingular Enriques surface in
characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties
but are not irreducible symplectic as the hodge number h2,0 > 1, even though a
supersingular Enriques surface is an irreducible symplectic variety. These are
the classes of varieties which appear only in characteristic 2 and they show that
the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic
2. It also gives examples of varieties with trivial canonical class which are
neither irreducible symplectic nor Calabi-Yau, thereby showing that there are
strictly more classes of simply connected varieties with trivial canonical class
in characteristic 2 than over C as given by Beauville-Bogolomov decomposition
theorem.
acknowledgement: I would like to thank M. Zdanwociz for various mathematical discussions
which lead to this article, Tamas Hausel for hosting me in his research group at
IST Austria and the anonymous referee for their helpful suggestions and comments.
This research has received funding from the European Union's Horizon 2020 Marie
Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology
Austria IST-PLUS Grant No. 754411.
article_number: '102957'
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface. Bulletin des Sciences Mathematiques. 2021;167(03). doi:10.1016/j.bulsci.2021.102957
apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a
supersingular Enriques surface. Bulletin Des Sciences Mathematiques. Elsevier.
https://doi.org/10.1016/j.bulsci.2021.102957
chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a
Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques. Elsevier,
2021. https://doi.org/10.1016/j.bulsci.2021.102957.
ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface,” Bulletin des Sciences Mathematiques, vol. 167, no. 03.
Elsevier, 2021.
ista: Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.
mla: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular
Enriques Surface.” Bulletin Des Sciences Mathematiques, vol. 167, no. 03,
102957, Elsevier, 2021, doi:10.1016/j.bulsci.2021.102957.
short: T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).
date_created: 2021-02-21T23:01:20Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-07T13:47:48Z
day: '01'
department:
- _id: TaHa
doi: 10.1016/j.bulsci.2021.102957
ec_funded: 1
external_id:
arxiv:
- '2010.08976'
isi:
- '000623881600009'
intvolume: ' 167'
isi: 1
issue: '03'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2010.08976
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Bulletin des Sciences Mathematiques
publication_identifier:
issn:
- 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pathologies of the Hilbert scheme of points of a supersingular Enriques surface
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 167
year: '2021'
...
---
_id: '7436'
abstract:
- lang: eng
text: 'For an ordinary K3 surface over an algebraically closed field of positive
characteristic we show that every automorphism lifts to characteristic zero. Moreover,
we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one
correspondence with the Fourier-Mukai partners of the geometric generic fiber
of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai
partners of the K3 surfaces with Picard rank two and with discriminant equal to
minus of a prime number, in terms of the class number of the prime, holds over
a field of positive characteristic as well. We show that the image of the derived
autoequivalence group of a K3 surface of finite height in the group of isometries
of its crystalline cohomology has index at least two. Moreover, we provide a conditional
upper bound on the kernel of this natural cohomological descent map. Further,
we give an extended remark in the appendix on the possibility of an F-crystal
structure on the crystalline cohomology of a K3 surface over an algebraically
closed field of positive characteristic and show that the naive F-crystal structure
fails in being compatible with inner product. '
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 2019;24:1135-1177. doi:10.25537/dm.2019v24.1135-1177
apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive
characteristic. Documenta Mathematica. EMS Press. https://doi.org/10.25537/dm.2019v24.1135-1177
chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive
Characteristic.” Documenta Mathematica. EMS Press, 2019. https://doi.org/10.25537/dm.2019v24.1135-1177.
ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,”
Documenta Mathematica, vol. 24. EMS Press, pp. 1135–1177, 2019.
ista: Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 24, 1135–1177.
mla: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.”
Documenta Mathematica, vol. 24, EMS Press, 2019, pp. 1135–77, doi:10.25537/dm.2019v24.1135-1177.
short: T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.
date_created: 2020-02-02T23:01:06Z
date_published: 2019-05-20T00:00:00Z
date_updated: 2023-10-17T07:42:21Z
day: '20'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.25537/dm.2019v24.1135-1177
external_id:
arxiv:
- '1809.08970'
isi:
- '000517806400019'
file:
- access_level: open_access
checksum: 9a1a64bd49ab03fa4f738fb250fc4f90
content_type: application/pdf
creator: dernst
date_created: 2020-02-03T06:26:12Z
date_updated: 2020-07-14T12:47:58Z
file_id: '7438'
file_name: 2019_DocumMath_Srivastava.pdf
file_size: 469730
relation: main_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1135-1177
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On derived equivalences of k3 surfaces in positive characteristic
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
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...