A note on certain Tannakian group schemes

Sanjay Amrutiya

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 1, page 21-29
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Amrutiya, Sanjay. "A note on certain Tannakian group schemes." Archivum Mathematicum 056.1 (2020): 21-29. <http://eudml.org/doc/295086>.

@article{Amrutiya2020,
abstract = {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.},
author = {Amrutiya, Sanjay},
journal = {Archivum Mathematicum},
keywords = {F-fundamental group scheme; Frobenius-finite Vector bundles},
language = {eng},
number = {1},
pages = {21-29},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on certain Tannakian group schemes},
url = {http://eudml.org/doc/295086},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Amrutiya, Sanjay
TI - A note on certain Tannakian group schemes
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 1
SP - 21
EP - 29
AB - 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.
LA - eng
KW - F-fundamental group scheme; Frobenius-finite Vector bundles
UR - http://eudml.org/doc/295086
ER -

References

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