Related papers: Standard Norm Varieties for Milnor Symbols mod p

By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb Z[a_1,a_2,\dots]$, ${\rm deg}(a_i)=2i$. In this paper we solve a…

For prime $p\ge 7$, by using Baker's method we obtain two explicit bounds in terms of $p$ for the $j$-invariant of an integral point on $X_{\ns}^{+}(p)$ which is the modular curve of level $p$ corresponding to the normalizer of a non-split…

It was shown by Kuznetsov that complete intersections of $n$ generic quadrics in ${\mathbb P}^{2n-1}$ are related by Homological Projective Duality to certain non-commutative (Clifford) varieties which are in some sense birational to double…

We want to bound the symbol length of classes in ${_{2^{m-1}}Br}(F)$ which are represented by tensor products of 5 or 6 cyclic algebras of degree $2^m$. The main ingredients are the chain lemma for quadratic forms, a form of a generalized…

We compute the one-loop renormalization of the Planck mass for type II string theories compactified to four dimensions on symmetric orbifolds that preserve ${\cal N}=2$ supersymmetry. Depending on the orbifold, the effect can be as large as…

In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes either anisotropic or metabolic over all extensions of the…

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

We announce a very general statement involving the rational quartic residue symbol $(m/p)_4$ and, more generally, Legendre symbols of the type ${a+b\sqrt{m}/p$. We show how our main theorem can be used to produce many older results such as…

For two varieties of dimension $5$ constructed as double covers of ${\mathbb P}^5$ branched along the union of $12$ hyperplanes, we prove that the number of points over ${\mathbb F}_p$ can be expressed in terms of Artin symbols and the…

We introduce a simple criterion to check coercivity of bilinear forms on subspaces of Hilbert-spaces and Banach-spaces. The presented criterion allows to derive many standard and non-standard variants of Poincar\'e- and Friedrichs-type…

We study the mod $p^r$ Milnor $K$-groups of $p$-adically complete and $p$-henselian rings, establishing in particular a Nesterenko-Suslin style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes…

Two-dimensional N=1,2 supersymmetric chiral models and their dual extensions are introduced and canonically quantized. Working within a superspace formalism, the non-manifest invariance under 2D-superPoincare' transformations is proven. The…

Virasoro-type symmetries and their roles in solvable models are reviewed. These symmetries are described by the two-parameter Virasoro-type algebra $Vir_{p,q}$ by choosing the parameters p and q suitably.

In this article, certain symmetry identities for the 2-variable Apostol type polynomials are derived. By taking suitable values of parameters and indices, the symmetry identities for the special cases of the 2-variable Apostol type…

We show that over any field $F$ of $\operatorname{char}(F)=2$ and 2-rank $n$, there exist $2^n$ bilinear $n$-fold Pfister forms that have no slot in common. This answers a question of Becher's in the negative. We provide an analogous result…

Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on…

We consider the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander classes $BS_{\rho, \rho}^m$, $0 < \rho < 1$. In this paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary when we consider the…

We prove that if the maximal dimension of an anisotropic homogeneous polynomial form of prime degree $p$ over a field $F$ with $\operatorname{char}(F)=p$ is a finite integer $d$ greater than 1 then the symbol length of $p$-algebras of…

We show that for all $n\geq 3$ and all primes $p$ there are infinitely many simplicial toric varieties of codimension $n$ in the $2n$-dimensional affine space whose minimum number of defining equations is equal to $n$ in characteristic $p$,…

We prove that if $G$ is finite 2-generated $p$-group of nilpotence class at most 2 then the group algebra of $G$ with coefficients in the field with $p$ elements determines $G$ up to isomorphisms.