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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.