dc.identifier.uri |
http://dx.doi.org/10.15488/13753 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/13863 |
|
dc.contributor.author |
Floccari, Salvatore
|
|
dc.date.accessioned |
2023-05-26T09:15:31Z |
|
dc.date.available |
2023-05-26T09:15:31Z |
|
dc.date.issued |
2022 |
|
dc.identifier.citation |
Floccari, S.: Galois representations on the cohomology of hyper-Kähler varieties. In: Mathematische Zeitschrift 301 (2022), Nr. 1, S. 893-916. DOI: https://doi.org/10.1007/s00209-021-02923-3 |
|
dc.description.abstract |
We show that the André motive of a hyper-Kähler variety X over a field K⊂ C with b2(X) > 6 is governed by its component in degree 2. More precisely, we prove that if X1 and X2 are deformation equivalent hyper-Kähler varieties with b2(Xi) > 6 and if there exists a Hodge isometry f: H2(X1, Q) → H2(X2, Q) , then the André motives of X1 and X2 are isomorphic after a finite extension of K, up to an additional technical assumption in presence of non-trivial odd cohomology. As a consequence, the Galois representations on the étale cohomology of X1 and X2 are isomorphic as well. We prove a similar result for varieties over a finite field which can be lifted to hyper-Kähler varieties for which the Mumford–Tate conjecture is true. |
eng |
dc.language.iso |
eng |
|
dc.publisher |
Berlin, Heidelberg : Springer |
|
dc.relation.ispartofseries |
Mathematische Zeitschrift 301 (2022), Nr. 1 |
|
dc.rights |
CC BY 4.0 Unported |
|
dc.rights.uri |
https://creativecommons.org/licenses/by/4.0 |
|
dc.subject |
Galois representations |
eng |
dc.subject |
Hodge theory |
eng |
dc.subject |
Hyper-Kähler varieties |
eng |
dc.subject |
Motives |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
Galois representations on the cohomology of hyper-Kähler varieties |
eng |
dc.type |
Article |
|
dc.type |
Text |
|
dc.relation.essn |
1432-1823 |
|
dc.relation.issn |
0025-5874 |
|
dc.relation.doi |
https://doi.org/10.1007/s00209-021-02923-3 |
|
dc.bibliographicCitation.issue |
1 |
|
dc.bibliographicCitation.volume |
301 |
|
dc.bibliographicCitation.firstPage |
893 |
|
dc.bibliographicCitation.lastPage |
916 |
|
dc.description.version |
publishedVersion |
|
tib.accessRights |
frei zug�nglich |
|