Related papers: Parametrization of Formal Norm Compatible Sequence…
In this article we study the Honda-Tate theory for log abelian varieties over an fs log point $S=(\mathrm{Spec}(\mathbf{k}),M_S)$ for $\mathbf{k}=\mathbb{F}_q$ a finite field, generalizing the classical Honda-Tate theory for abelian…
A class of covariant gauges allowing one to interpolate between the Landau, the maximal Abelian, the linear covariant and the Curci-Ferrari gauges is discussed. Multiplicative renormalizability is proven to all orders by means of algebraic…
We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents,…
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be…
We prove a generalization of Gabrielov's rank theorem for families of rings of power series which we call W-temperate. Examples include the families of complex analytic functions and of Eisenstein series. As a Corollary, we provide rank…
The local equivariant Tamagawa number conjecture (local ETNC) for a motive predicts a precise relationship between the local arithmetic complex and the root numbers which appear in the (conjectural) functional equations of the…
This article is the last one about the isomorphism between Lubin-Tate and Drinfeld towers. We prove the existence of an isomorphism between the compactly supported etale cohomology of the Lubin-Tate and Drinfeld towers, and more generally…
Following Weinstein, Boyarchenko-Weinstein and Imai-Tsushima, we construct a family of affinoids in the Lubin-Tate perfectoid space and formal models such that the cohomology of the reduction of each formal model realizes the local…
An analysis using a composition of currently-accepted theories is given. Starting with a synthesis of what may be generically termed ``paths'', analysis of representations for these ``paths'' is developed. Foreground and background…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…
We formulate a classification conjecture for conformally invariant families of measures on simple loops that builds on a conjecture of Kontsevich and Suhov. The main example in this class of objects was constructed by Werner as boundaries…
For supersymmetric extensions of the Standard Model we construct some expressions that include Yukawa couplings for the third and second generations and receive relatively small quantum corrections. This implies that they slightly depend on…
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
We study a generalization of Serre--Tate theory of ordinary abelian varieties and their deformation spaces. This generalization deals with abelian varieties equipped with additional structures. The additional structures can be not only an…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
Thom polynomials provide universal formulas for the fundamental class of singularity loci in terms of characteristic classes. Ohmoto extended this notion to SSM-Thom polynomials, which refine this description by capturing the richer…
This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…