Related papers: Reconstruction of Function Fields from their pro-l…

Let $K$ be the function field of a curve over a finite field of odd characteristic. We investigate using $L$-functions of Galois extensions of $K$ to effectively recover $K$. When $K$ is the function field of the projective line with four…

Let $K$ be a finite extension of the $p$-adic numbers $\mathbb Q_p$ with ring of integers $\mathcal O_K$, $\mathcal X$ a regular scheme, proper, flat, and geometrically irreducible over $\mathcal O_K$ of dimension $d$, and $\mathcal X_K$…

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…

We consider function fields of transcendence degree at least 2 over algebraic closures of finite fields, and describe a functorial way to recover such function fields form their pro-l Galois theory.

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a…

We introduce a functor $\mathfrak{M}:\mathbf{Alg}\times\mathbf{Alg}^\mathrm{op}\rightarrow\mathrm{pro}\text{-}\mathbf{Alg}$ constructed from representations of $\mathrm{Hom}_\mathbf{Alg}(A,B\otimes ? )$. As applications, the following items…

Let $K$ be a field with a discrete valuation, and let $p$ and $\ell$ be (possibly equal) primes which are not necessarily different from the residue characteristic. Given a superelliptic curve $C : y^p = f(x)$ which has split degenerate…

In this paper we generalize an argument of Neukirch from birational anabelian geometry to the case of arithmetic curves. In contrast to the function field case, it seems to be more complicate to describe the position of decomposition groups…

We give an explicit algebraic description, based on prismatic cohomology, of the algebraic K-groups of rings of the form $O_K/I$ where $K$ is a p-adic field and $I$ is a non-trivial ideal in the ring of integers $O_K$; this class includes…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\in\mathbb Z$, associated with the Matsubara frequencies $\nu_{k}=2\pi…

We prove that the $K$-group of reciprocity functors, defined by F. Ivorra and the first author, vanishes over a perfect field as soon as one of the reciprocity functors is $\mathbb{G}_a$ and one is an abelian variety.

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

We unify various \'etale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semigroup. 3) Steinberg's reconstruction from a groupoid ring.…

We develop an explicit theory of formal modular forms over arbitrary number fields $K$, as functions of modular points. We define modular points for $\Gamma_0({\mathfrak n})$ and $\Gamma_1({\mathfrak n})$, where the level ${\mathfrak n}$ is…

Let $A/K$ be an abelian variety with real multiplication defined over a $p$-adic field $K$ with $p>2$. We show that $A/K$ must have either potentially good or potentially totally toric reduction. In the former case we give formulas of the…

In this paper we apply the hyper-K\"ahler quotient construction to Lie groups with a left invariant hyper-K\"ahler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known…

Using algebraic and topological K-theory together with complex C^*-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and…

Let $K$ be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over $K$ whose $\ell$-power torsion fields are arithmetically constrained for some rational prime $\ell$. Such arithmetic…

Given a regular function $\phi$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $\phi$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix…