Add to ORKGWe study a symplectic variant of algebraic $K$-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of $\mathbf{Q}$. We compute this action explicitly. The representations we see are extensions of Tate twists $\mathbf{Z}_p(2k-1)$ by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.Comment: 64 pages, final accepted versio
The Lichtenbaum--Quillen conjecture (LQC) relates special values of zeta functions to algebraic K-th...
AbstractTextLet p be a prime, and q a power of p. Using Galois theory, we show that over a field K o...
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic c...
In this paper we will discuss the absolute Galois group, the Galois group of Q where Q is an algebra...
We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic ext...
We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic ext...
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over...
Let $K$ be a number field, $f\in K[x]$ and $\alpha\in K$. A recent conjecture of Andrews and Petsche...
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over...
AbstractLet K2Z where Z is the ring of integers of a number field k. We define a subgroup H20k of in...
Let K be a number field and A be a g-dimensional abelian variety over K. For every prime ℓ, the ℓ-ad...
The goal of this thesis project is to study the Cp-semilinear representation given by the p-Tate mod...
We introduce $\ell$-Galois special subvarieties as an $\ell$-adic analog of the Hodge-theoretic noti...
We construct infinitely many abelian surfaces $A$ defined over the rational numbers such that, for $...
29 pagesInternational audienceLet p be an odd prime, K a finite extension of Q_p , G_K = Gal(Kbar/K)...
The Lichtenbaum--Quillen conjecture (LQC) relates special values of zeta functions to algebraic K-th...
AbstractTextLet p be a prime, and q a power of p. Using Galois theory, we show that over a field K o...
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic c...
In this paper we will discuss the absolute Galois group, the Galois group of Q where Q is an algebra...
We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic ext...
We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic ext...
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over...
Let $K$ be a number field, $f\in K[x]$ and $\alpha\in K$. A recent conjecture of Andrews and Petsche...
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over...
AbstractLet K2Z where Z is the ring of integers of a number field k. We define a subgroup H20k of in...
Let K be a number field and A be a g-dimensional abelian variety over K. For every prime ℓ, the ℓ-ad...
The goal of this thesis project is to study the Cp-semilinear representation given by the p-Tate mod...
We introduce $\ell$-Galois special subvarieties as an $\ell$-adic analog of the Hodge-theoretic noti...
We construct infinitely many abelian surfaces $A$ defined over the rational numbers such that, for $...
29 pagesInternational audienceLet p be an odd prime, K a finite extension of Q_p , G_K = Gal(Kbar/K)...
The Lichtenbaum--Quillen conjecture (LQC) relates special values of zeta functions to algebraic K-th...
AbstractTextLet p be a prime, and q a power of p. Using Galois theory, we show that over a field K o...
A result due to R. Greenberg gives a relation between the cardinality of Selmer groups of elliptic c...