In this paper we give an extension of the Cartier-Gabriel-Kostant structure theorem to Hopf algebroids.
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17 results for “Cartier”
Defines formal vertex laws related to Lie conformal algebras.
problem No specific problem stated; focuses on definitions and proofs.
method Definitions and proofs of vertex/conformal versions of classical Lie theory results.
result Proves vertex/conformal versions of important Lie theory results.
New theorem clarifies seasonalities and cycles in time series.
problem Clarifying seasonalities and cycles in time series data.
method Application of a recent theorem by Cartier and Perrin, with computer experiments.
result Clear-cut definition and easy implementation of seasonalities and cycles.
We review the extent to which the universal enveloping algebra of a Lie-Rinehart algebra resembles a Hopf algebra, and refer to this structure as a Rinehart bialgebra. We then prove a Cartier-Milnor-Moore type theorem for such Rinehart bialgebras.
This study connects ReLU neural networks to toric geometry to analyze function realization.
problem Determining which continuous piecewise linear functions can be realized by ReLU neural networks.
method Established a connection between toric geometry and ReLU neural networks, defining key structures like the ReLU fan, toric variety, and Cartier divisor.
result Proved a criterion for functions realizable by unbiased shallow ReLU networks using intersection numbers.
An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of j…
Let X be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): X and all its subvarieties are of general type and the canonical divisor K_X is ample at smooth points and Kawamata log terminal points of X, provided that K_X is Q-Cartier, no Calabi-Yau variety…
The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as a byproduct a new understanding of the means of returns, of the beta coefficient…
The paper studies stability of CR structures on compact manifolds.
problem Stability of CR structures on compact manifolds.
method Smooth deformations and projective embeddings.
result Nearby structures still admit projective CR embeddings.
A new standpoint on financial time series, without the use of any mathematical model and of probabilistic tools, yields not only a rigorous approach of trends and volatility, but also efficient calculations which were already successfully applied in automatic control and in signal processing. It is based on a theorem d…
Extends distribution algebra concept to Lie groupoids.
problem Distribution algebra on Lie groupoids.
method Construction of convolution C_c(M)/R-bialgebra associated with Lie groupoid adjoint action.
result Extension of Cartier-Gabriel decomposition to Lie groupoids.
We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice…
New findings link K-semistability to volume minimization for Fano varieties.
problem K-semistability of Fano varieties and its relation to volume minimization.
method Equivariant volume minimization over -Gorenstein klt singularities.
result K-semistability of is equivalent to normalized volume minimization at the canonical valuation .
The paper proves volume minimization for Kähler-Einstein metrics and related structures.
problem Volume minimization for Kähler-Einstein metrics and related structures.
method Volume minimization using real valuations centered at the vertex of the affine cone.
result The normalized volume is globally minimized at the canonical valuation.
Solves differentiation for Lie ∞-groups using formal groupoids.
problem Differentiation of Lie ∞-groups.
method Develops homotopy theory of formal ∞-groupoids and analyzes Dold-Kan adjunction for cosimplicial algebras.
result Differentiation functor from finite-dimensional Lie ∞-groups to finite-type Lie ∞-algebras is homotopically well-behaved.
The paper calculates the dimension of the image of the Abel map for normal surface singularities.
problem Calculating the dimension of the image of the Abel map for normal surface singularities.
method Provides combinatorial formulae for the dimension of the image of the Abel map.
result Combinatorial formulae for the dimension of the image of the Abel map.
Researchers developed a rigorous mathematical formulation of functional integration for fields on paracompact manifolds.
problem Overcoming the problematic aspect of measures in the space of fields.
method Using Schwartz-Sobolev spaces, open coverings with subordinate partition-of-unity test functions, and convolution operations.
result Validated the basic assumption of differential geometry that fields live on differentiable manifolds.