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of 41
pro vyhledávání: '"Lavrenov, Andrei"'
We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory analogue of
Externí odkaz:
http://arxiv.org/abs/2409.14099
The main result of the present paper is bounded elementary generation of the Steinberg groups $\mathrm{St}(\Phi,R)$ for simply laced root systems $\Phi$ of rank $\ge 2$ and arbitrary Dedekind rings of arithmetic type. Also, we prove bounded generatio
Externí odkaz:
http://arxiv.org/abs/2307.05526
Autor:
Lavrenov, Andrei, Petrov, Victor
We prove that inner forms of a variety of Borel subgroups have isomorphic motives with respect to the second Morava K-theory if and only if the corresponding Tits algebras and Rost invariants coincide. This extends Panin's results on interrelationshi
Externí odkaz:
http://arxiv.org/abs/2306.13605
Let $k$ be an arbitrary field. In this paper we show that in the linear case ($\Phi=\mathsf{A}_\ell$, $\ell \geq 4$) and even orthogonal case ($\Phi = \mathsf{D}_\ell$, $\ell\geq 7$, $\mathrm{char}(k)\neq 2$) the unstable functor $\mathrm{K}_2(\Phi,
Externí odkaz:
http://arxiv.org/abs/2110.11087
Publikováno v:
In Advances in Mathematics June 2024 446
We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these results to stu
Externí odkaz:
http://arxiv.org/abs/2011.14720
We prove the centrality of $\mathrm{K}_2 (\mathsf{F}_4, \,R)$ for an arbitrary commutative ring $R$. This completes the proof of the centrality of $\mathrm K_2(\Phi,\, R)$ for any root system $\Phi$ of rank $\geq 3$. Our proof uses only elementary lo
Externí odkaz:
http://arxiv.org/abs/2009.03999
Autor:
Lavrenov, Andrei, Sinchuk, Sergey
Publikováno v:
Doc. Math. 25 (2020), pp. 767--809
We prove the Horrocks theorem for unstable even-dimensional orthogonal Steinberg groups. The Horrocks theorem for Steinberg groups is one of the principal ingredients needed for the proof of the $\mathrm{K}_2$-analogue of Serre's problem, whose posit
Externí odkaz:
http://arxiv.org/abs/1909.02637
In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products $G \otimes H$ and tensor squares $G \otimes G$. Using these r
Externí odkaz:
http://arxiv.org/abs/1710.02330
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