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1
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Stable cohomology of alternating groups

100%
Bogomolov F., Böhning C.
Open Mathematics
|
2014
|
tom 12
|
nr 2
212-228
EN
We determine the stable cohomology groups ($$H_S^i \left( {{{\mathfrak{A}_n ,\mathbb{Z}} \mathord{\left/ {\vphantom {{\mathfrak{A}_n ,\mathbb{Z}} {p\mathbb{Z}}}} \right. \kern-\nulldelimiterspace} {p\mathbb{Z}}}} \right)$$ of the alternating groups $$\mathfrak{A}_n$$ for all integers n and i, and all odd primes p.
2
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Linear bounds for levels of stable rationality

76%
Bogomolov F., Böhning C., Graf von Bothmer H.-C.
Open Mathematics
|
2012
|
tom 10
|
nr 2
466-520
EN
Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.
3
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Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

76%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1157-1163
EN
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
4
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Unramified cohomology of alternating groups

64%
Bogomolov F., Petrov T.
Open Mathematics
|
2011
|
tom 9
|
nr 5
936-948
EN
We prove vanishing results for the unramified stable cohomology of alternating groups.
5
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Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

64%
Trepalin A.
Open Mathematics
|
2014
|
tom 12
|
nr 2
229-239
EN
Let $$\Bbbk$$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $$\Bbbk$$. Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $$\Bbbk$$ is algebraically closed. In this paper we prove that $${{\mathbb{P}_\Bbbk ^2 } \mathord{\left/ {\vphantom {{\mathbb{P}_\Bbbk ^2 } G}} \right. \kern-\nulldelimiterspace} G}$$ is rational for an arbitrary field $$\Bbbk$$ of characteristic zero.
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