Related papers: Open descent and strong approximation
We prove the exactness of a descent sequence relating the algebraic cobordism groups of a scheme and its envelopes. Analogous sequences for Chow groups and K-theory were previously proved by Gillet.
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
In this paper, we develop the higher descent equations for higher gauge theories within the framework of 2-term $L_{\infty}$ algebras. Starting from a multilinear symmetric invariant polynomial, we construct a family of higher Chern-Simons…
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective…
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich, Haynes and Velani in 2015. Hitherto,…
This article studies descent theory in the setting of Berkovich spaces. We give sufficient conditions for a given fibered category over the category of k-affinoid algebras to be a stack for the Berkovich analogue of the faithfully-flat…
As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…
In his article "Arithmetic Fujita Approximations", Huayi Chen introduces the notion of an approximable graded algebra and asks if any such algebra is a subalgebra of the graded section ring of a big line bundle on an algebraic variety. We…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof…
In this book we collect many different and useful facts around gradient descent method. First of all we consider gradient descent with inexact oracle. We build a general model of optimized function that include composite optimization…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We extend Greenberg's strong approximation theorem to schemes of finite presentation over valuation rings with arbitrary value group, using the ultraproduct method of Becker, Denef, Lipshitz and van den Dries. As an application, we prove a…
A very simple but useful almost sure convergence theorem of probability is given.
In differential algebra, a proper scheme $X$ defined over an algebraically closed field $K$ with a derivation $\partial$ on it descends to the field of constants $K^\partial$ if $X$ itself lifts the derivation $\partial$. This is a result…
We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory,…
We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…