Related papers: On functional equations of Euler systems

In this paper a Kummer theory of division points over rank one Drinfeld A=Fq[T]-modules defined over global function fields was given. The results are in complete analogy with the classical Kummer theory of division points over the…

We prove a motivic refinement of a result of Weil, Deligne and Raynaud on the existence of strongly compatible systems associated to abelian varieties. More precisely, given an abelian variety $A$ over a number field $\mathrm{E}\subset…

In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…

We consider Abelian extensions of global symmetries of the form $A \to G \to K$, with $A$ finite (and similar higher-group structures). For a quantum field theory $\mathcal{T}$ with symmetry $G$, we compare gauging $G$ directly with gauging…

Fix a relative quadratic extension E/F of totally real number rields and let G denote the Galois group of order 2. Let S be a finite set of primes of F containing the infinite primes and all those which ramify in E, let S_E denote the…

Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conjectures about their rationality properties. Moreover, if K…

It is well known that Euler experimentally discovered the functional equation of the Riemann zeta function. Indeed he detected the fundamental $s\mapsto 1-s$ invariance of $\zeta(s)$ by looking only at special values. In particular, via…

Explicit solutions of the cubic Fermat equation are constructed in ring class fields $\Omega_f$, with conductor $f$ prime to $3$, of any imaginary quadratic field $K$ whose discriminant satisfies $d_K \equiv 1$ (mod $3$), in terms of the…

We introduce and study subalgebra cotype zeta functions, multivariate zeta functions enumerating fixed-index subalgebras of $R$-algebras of a given cotype. This generalizes and unifies previous works on subalgebra zeta functions and cotype…

Let $K$ be a function field of one variable over a finite field $\mathbb{F}$. Weil's celebrated theorem states that the congruent zeta function of $K/\mathbb{F}$ is determined by the $\mathrm{Gal}(\overline{\mathbb{F}}/\mathbb{F})$-module…

Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner…

The aim of this paper is to give a full detail of the proof given by Harder of a theorem on the denominator of the Eisenstein class for $\mathrm{SL}_2(\mathbb{Z})$ and to show that the theorem has some interesting applications including the…

We lift the Euler characteristic of a nearly perfect complex to a relative algebraic K-group by passing to its l-adic Euler characteristics.

In this paper, we determine the connective K-cohomology with reality of elementary abelian $2$-groups as a module over $\mathbb{Z}[v_1,a]$, where $v_1$ is the equivariant Bott class and $a$ the Euler class of the sign representation. This…

We define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when…

We prove that the theory of the $p$-adics ${\mathbb Q}_p$ admits elimination of imaginaries provided we add a sort for ${\rm GL}_n({\mathbb Q}_p)/{\rm GL}_n({\mathbb Z}_p)$ for each $n$. We also prove that the elimination of imaginaries is…

We give a short proof of the anticyclotomic analogue of the "strong" main conjecture of Kurihara on Fitting ideals of Selmer groups for elliptic curves with good ordinary reduction under mild hypotheses. More precisely, we completely…

Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…

We study the behaviour of the Stark conjecture for an abelian extension K/k of totally real number fields as K varies in a cyclotomic Z_p-tower. We consider possible strengthenings of the natural norm-coherence in the tower of putative…

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…