Let G be a simple algebraic group defined over the global field k. In this paper, we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of G, with specified local behavior at a finite set of places of k and unramified elsewhere. This sum is expressed as the product of the values of modified Artin L-functions at neg...

Throughout this paper, G denotes a fixed, not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series (beginning with [L9],[L10]) which attempts to develop a theory of character sheaves on G. Assume now that k is an algebraic closure of a finite field Fq and that G has a fixed Fq-structure with Frobenius map F . Let (L, S, E , φ0) ...

1. Residues . ..... ........ .... ... .... 54 2. ir-discrete distributions ............... . .. . . .. . 58 3. Admissible families of operators .......... ............. 67 4. The main formula ............. ... ............ 74 5. Completion of the induction argument .................... 83 6. Cuspidal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7. Conclusions ..............

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...

the aim of this paper is to study the $(alpha‎, ‎gamma)$-prolongation of central extensions‎. ‎we obtain the obstruction theory for $(alpha‎, ‎gamma)$-prolongations and classify $(alpha‎, ‎gamma)$-prolongations thanks to low-dimensional cohomology groups of groups‎.

the aim of this paper is to study co-prolongations of central extensions. we construct the obstruction theory forco-prolongations and classify the equivalence classes of these by kernels of homomorphisms between 2-dimensional cohomology groups of groups.

We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

Abstract. We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation π of GSp 4 (F ), where F is a non-archimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply...

We shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap. As an application, we show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. Introduction Let U be a ...