Related papers: Hasse Principle for G-quadratic forms

We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to 28 defined over $\mathbb{Q}$.

Let $F$ be a field. Following the resolution of Milnor's conjecture relating the graded Witt ring of $F$ to its mod-2 Milnor $K$-theory, a major problem in the theory of symmetric bilinear forms is to understand, for any positive integer…

Segal's hypothesis that physical theories drift toward simple groups follows from a general quantum principle and suggests a general quantization process. I general-quantize the scalar meson field in Minkowski space-time to illustrate the…

In this article we show how the Dedekind-Hasse criterion may be applied to prove a simple result about quadratic number fields that usually is derived as a consequence of the theory of ideals and ideal classes.

This paper proves the Hasse principle and weak approximation for varieties defined by the smooth intersection of three quadratics in at least 19 variables, over arbitrary number fields.

The aim of this note is to show that the "usual" proof of the Maschke Theorem in the case of a real and complex field can not be generalized at least to the case of a field of rational functions on a non-singular curve.

We review a notion of completeness in QFT arising from the analysis of basic properties of the set of operator algebras attached to regions. In words, this completeness asserts that the physical observable algebras produced by local degrees…

Deciding whether or not two polynomials have isomoprhic splitting fields over the rationals is the Field Isomorphism Problem. We consider polynomials of the form $f_n(x) = x^4-nx^3-6x^2+nx+1$ with $n \neq 3$ a positive integer and we let…

A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields…

We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…

We show that the theorem of Ellenberg and Venkatesh on representation of integral quadratic forms by integral positive definite quadratic forms is valid under weaker conditions on the represented form.

The Hasse principle and weak approximation is established for equations of the shape P(t)=N(x_1,x_2,x_3,x_4), where P is an irreducible quadratic polynomial in one variable and N is a norm form associated to a quartic extension of the…

For any positive integer M we show that there are infinitely many real quadratic fields that do not admit M-ary universal quadratic forms (without any restriction on the parity of their cross coefficients).

We say that two abelian varieties $A$ and $A'$ defined over a field $F$ are polyquadratic twists if they are isogenous over a Galois extension of $F$ whose Galois group has exponent dividing $2$. Let $A$ and $A'$ be abelian varieties…

Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$…

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number…

We use the theory of Harbater-Katz-Gabber curves to derive a generalization of the Hasse-Arf theorem for complete local field extensions in positive characteristic.

In this note, we use the isomorphism of the ring of $G$-circulant matrices over a field $k$ with the group ring $k[G]$ to derive a very short proof of the Classical Maschke Theorem.

I make some remarks on Hodge symmetry, and prove for instance that if $k$ is a perfect field of characteristic $p>0$ and $X/k$ smooth, proper and Hodge-Witt scheme, and Hodge de Rham sequence of $X$ degenerates at $E_1$ and $X$ has…

As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the…