Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeometrie non-commutative, formule des traces et conducteur de Bloch
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This text is based on a talk by the first named author at the first congress of the SMF (Tours, 2016). We present Blochs conductor formula, which is a conjectural formula describing the change of topology in a family of algebraic varieties when the parameter specialises to a critical value. The main objective of this paper is to describe a general approach to the resolution of Blochs conjecture based on techniques from both non-commutative geometry and derived geometry.
rate research
Read More
This article is a brief presentation of results surrounding the fundamental gap. We begin by recalling Bakry-Emery geometry and demonstrate connections between eigenvalues of the Laplacian with the Dirichlet and Neumann boundary conditions. We then show a connection between the fundamental gap and Bakry-Emery geometry, concluding with a presentation of the key ideas in Andrewss and Clutterbucks proof of the fundamental gap conjecture. We conclude with a presentation of results for the fundamental gap of triangles and simplices.
In this paper, we continue our project of defining and studying the infinitesim
We describe a conjectural construction (in the spirit of Hilberts 12th problem) of units in abelian extensions of certain base fields which are neither totally real nor CM. These base fields are quadratic extensions with exactly one complex place of a totally real number field F, and are referred to as Almost Totally real (ATR) extensions. Our construction involves certain null-homologous topological cycles on the Hilbert modular variety attached to F. The special units are the images of these cycles under a map defined by integration of weight two Eisenstein series on GL_2(F). This map is formally analogous to the higher Abel-Jacobi maps that arise in the theory of algebraic cycles. We show that our conjecture is compatible with Starks conjecture for ATR extensions; it is, however, a genuine strengthening of Starks conjecture in this context since it gives an analytic formula for the arguments of the Stark units and not just for their absolute values. The last section provides numerical evidences for our conjecture.
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces of Sobolev spaces, the distance function, the notion of degree and a duality theorem, the variational formulation and conformal map in dimension 2, the metric on the boundary of a Lipschitz domain and polar geodesic coordinates and the Gauss-Bonnet formula and the positive mass theorem in dimension 3 and in the locally conformally flat case. And the Ricci flow. And fields and their relation to the equations.
This is the memoir of my habilitation thesis, defended on March 29 th, 2013 (Universite Paris XI).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
