| Title:
|
A note on certain Tannakian group schemes (English) |
| Author:
|
Amrutiya, Sanjay |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
21-29 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note, we prove that the $F$-fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the $F$-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the $F$-fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove that in this way, we do not get a non-trivial extension of the Nori fundamental group scheme for elliptic curves, unlike in characteristic zero. (English) |
| Keyword:
|
F-fundamental group scheme |
| Keyword:
|
Frobenius-finite Vector bundles |
| MSC:
|
14F05 |
| MSC:
|
14L15 |
| idZBL:
|
Zbl 07177877 |
| idMR:
|
MR4075885 |
| DOI:
|
10.5817/AM2020-1-21 |
| . |
| Date available:
|
2020-03-02T09:05:10Z |
| Last updated:
|
2020-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148033 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
