Related papers: The work of Laurent Lafforgue
This is the third paper in a series of papers studying intersection Floer theory of Lagrangians in the complement of a smooth divisor. We complete the construction of Floer homology for such Lagrangians.
A general discussion of equations with universal invariance for a scalar field is provided in the framework of Lagrangian theory of first-order systems.
We give a brief account of some of the most spectacular results established by James Maynard for which he has been awarded the Fields Medal.
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.
The basic theorem of the Lagrangian formulation for general superfield theory of fields (GSTF) is proved. The gauge transformations of general type (GTGT) and gauge algebra of generators of GTGT (GGTGT) as the consequences of the above…
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which…
We present the extension of the Lagrangian $loop$ representation in such a way to introduce matter fields. The partition function of lattice compact U(1) Gauge-Higgs model is expressed as a sum over closed as much as open surfaces. These…
As a simple corollary of a highly general framework for differential and difference Galois theory introduced by Y. Andre, we formulate a version of the Galois correspondence that applies over a difference field with arbitrary field of…
Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special…
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…
Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
This paper classifies Lagrangian fibrations over surfaces with compact total spaces up to fiberwise symplectomorphism identical on the base.
This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
The author surveys Galois theory of function fields with non-zero caracteristic and its relation to the structure of finite permutation groups and matrix groups.
A few families of counterexamples are provided to "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences", Journal of Computational…
We consider Floer homology associated to a pair of closed Lagrangian submanifolds that satisfy a monotonicty assumption. If the Lagrangians intersect cleanly we decribe two spectral sequences which help to compute their Floer homology. The…
We use the Jacquet-Langlands correspondence to generalize well-known congruence results of Mazur on Fourier coefficients and L-values of elliptic modular forms for prime level in weight 2 both to nonsquare level and to Hilbert modular…
We present a Lagrangian approach to counting degrees of freedom in first-order field theories. The emphasis is on the systematic attainment of a complete set of constraints. In particular, we provide the first comprehensive procedure to…
In this paper we investigate the connection between relations among various invariants of number field s $L^H$ coresponding to subgroups $H$ acting on $L$ and of linear relations among norm idempotents.