Related papers: Good reduction, bad reduction
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov…
We construct examples of (effective) closed orbifolds which are covered by manifolds, but not finitely so.
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…
We extend the homological method of quantization of generalized Drinfeld--Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.
To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of…
We construct examples of smooth proper rigid-analytic varieties admitting formal model with projective special fiber and violating Hodge symmetry for cohomology in degrees $\geq 3$. This answers negatively a question raised by Hansen and…
We construct a logarithmic model of connections on smooth quasi-projective $n$-dimensional geometrically irreducible varieties defined over an algebraically closed field of characteristic $0$. It consists of a good compactification of the…
The not-quite-Hamiltonian theory of singular reduction and reconstruction is described. This includes the notions of both regular and collective Hamiltonian reduction and reconstruction.
The general theory of the reduction in the number of coupling parameters is discussed. The method involves renormalization group invariant relations between couplings. It is more general than the imposition of symmetries. There are reduced…
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…
Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Harder's reduction theory provides filtrations of euclidean buildings that allow one to deduce cohomological and homological properties of S-arithmetic groups over global function fields. In this survey I will sketch the main points of…
In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM…
In this paper we will study an important but rather technical result which is called The Reduction Property. The result tells us how much arithmetical conservation there is between two arithmetical theories. Both theories essentially speak…