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Local-global principle for congruence subgroups of Chevalley groups

100%

Apte H., Stepanov A.

Open Mathematics

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2014

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tom 12

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nr 6

801-812

EN

Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.

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The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

100%

Borovoi M., González-Avilés C.

Open Mathematics

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2014

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tom 12

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nr 4

545-558

EN

We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.

3

Flasque resolutions of reductive group schemes

81%

González-Avilés C.

Open Mathematics

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2013

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tom 11

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nr 7

1159-1176

EN

We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.

Ograniczanie wyników

3 Open Mathematics

2 González-Avilés C.

1 Apte H.

1 Borovoi M.

1 Stepanov A.

2 2014

1 2013

Local-global principle for congruence subgroups of Chevalley groups

The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

Flasque resolutions of reductive group schemes