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pro vyhledávání: '"Clercq, Charles"'
Let $E/F$ be a finite field extension with every intermediate field being Galois over $F$. Given a reductive group $G$ over $F$ such that $G_E$ is of inner type, we define its A-upper motives. These motives are indecomposable and naturally related wi
Externí odkaz:
http://arxiv.org/abs/2403.11030
We establish the complete classification of Chow motives of projective homogeneous varieties for $p$-inner semi-simple algebraic groups, with coefficients in $\mathbb{Z}/p\mathbb{Z}$. Our results involve a new motivic invariant, the Tate trace of a m
Externí odkaz:
http://arxiv.org/abs/2302.12311
Autor:
De Clercq, Charles, Florence, Mathieu
Let $p$ be a prime. The goal of this article is to prove the Smoothness Theorem 5.1 (Theorem D), which notably asserts that a $(1,\infty)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smo
Externí odkaz:
http://arxiv.org/abs/2012.11027
Autor:
De Clercq, Charles, Florence, Mathieu
In this series of three articles, we study structural properties of smooth profinite groups, a class designed to extend classical Kummer theory for fields, with coefficients in $p$-primary roots of unity. Enhancing coefficients to arbitrary $G$-linea
Externí odkaz:
http://arxiv.org/abs/2009.11130
Akademický článek
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Autor:
De Clercq, Charles, Florence, Mathieu
Let $k$ be a field of characteristic $p>0$. Denote by $W_r(k)$ the ring of truntacted Witt vectors of length $r \geq 2$, built out of $k$. In this text, we consider the following question, depending on a given profinite group $G$. $Q(G)$: Does every
Externí odkaz:
http://arxiv.org/abs/1812.08068
Let $X$ be a scheme. Let $r \geq 2$ be an integer. Denote by $W_r(X)$ the scheme of Witt vectors of length $r$, built out of $X$. We are concerned with the question of extending (=lifting) vector bundles on $X$, to vector bundles on $W_r(X)$-promotin
Externí odkaz:
http://arxiv.org/abs/1807.04859
Motivic equivalence for algebraic groups was recently introduced in [9], where a characterization of motivic equivalent groups in terms of higher Tits indexes is given. As a consequence, if the quadrics associated to two quadratic forms have the same
Externí odkaz:
http://arxiv.org/abs/1802.03857
Autor:
De Clercq, Charles, Garibaldi, Skip
Publikováno v:
Journal of the London Mathematical Society 95 (2017), 567-585
The first author has recently shown that semisimple algebraic groups are classified up to motivic equivalence by the local versions of the classical Tits indexes over field extensions, known as Tits p-indexes. We provide in this article the complete
Externí odkaz:
http://arxiv.org/abs/1511.02538