Related papers: Fitting ideals of class groups for CM abelian exte…

If q : P -> M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra k of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo…

Let $K$ be a global function field and fix a place $\infty$ of $K$. Let $L/K$ be a finite real abelian extension, i.e. a finite, abelian extension such that $\infty$ splits completely in $L$. Then we define a group of elliptic units $C_L$…

Let $F$ be a totally real number field of class number one, and let $K$ be a CM-field with $F$ as its maximal real subfield. For each positive integer $N$, we construct a class group of certain binary quadratic forms over $F$ which is…

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…

The Jacobian group of a graph is a finite abelian group through which we can study the graph in an algebraic way. When the graph is a finite abelian covering of another graph, the Jacobian group is equipped with the action of the Galois…

The equivariant Tamagawa number conjecture (hereinafter called the eTNC) predicts close relationships between algebraic and analytic aspects of motives. In this paper, we prove a lot of new cases of the minus component of the eTNC for…

We study the existence of maximal ideals in preadditive categories defining an order $\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\preceq$, then there is no maximal ideal in the…

In our previous work, by using Kolyvagin derivatives of elliptic units, we constructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_i become "upper bounds" of the higher Fitting ideals of the one and two variable p-adic…

Let $E/F$ be an elliptic curve defined over a number field $F$ with complex multiplication by the ring of integers of an imaginary quadratic field $K$ such that the torsion points of $E$ generate over $F$ an abelian extension of $K$. In…

We prove that, for every modulus $\mathfrak{q}$, every class of the narrow ray class group $H_{\mathfrak{q}}(\mathbf{K})$ of an arbitrary number field $\mathbf{K}$ contains a product of three unramified prime ideals $\mathfrak{p}$ of degree…

We study the capitulation of $2$-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields $k =Q(\sqrt{pq_1q_2}, i)$, where $i=\sqrt{-1}$ and $q_1\equiv q_2\equiv-p\equiv-1 \pmod 4$ are different…

Let $K$ be an imaginary quadratic field with discriminant $d_K\leq-7$. We deal with problems of constructing normal bases between abelian extensions of $K$ by making use of singular values of Siegel functions. First, we show that a…

Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all…

In a previous paper we constructed rank and support variety theories for "quantum elementary abelian groups," that is, tensor products of copies of Taft algebras. In this paper we use both variety theories to classify the thick tensor…

For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is…

For an abelian variety $A$ over a number field $K$, we define the set of Tamagawa torsors of $A$ at a prime $v$ of $K$ to be the set of principal homogeneous spaces of $A$ over the completion $K_v$ of $K$ at $v$ that are split by an…

In this paper we examine the commutativity of ideal extensions. We introduce methods of constructing such extensions, in particular we construct a noncommutative ring T which contains a central and idempotent ideal I such that T/I is a…

We prove a uniform version of a finiteness conjecture due to Rasmussen and Tamagawa in the case of CM abelian varieties. This extends recent results concerning CM elliptic curves to CM abelian varieties of arbitrary dimension.

Let L/K be a finite Galois extension of number fields with Galois group G. Let p be a rational prime and let r be a non-positive integer. By examining the structure of the p-adic group ring Z_p[G], we prove many new cases of the p-part of…

We consider the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC). In their setup, a Tamagawa number is an element of a relative K-group. We show that this relative group agrees with an ordinary K-group, namely of…