WebThe Grothendieck trace formula may thus be translated into an equality between the alternating product of those elements and the class corresponding to theL-function. In this article, we will show that in the above reformulation of the Grothendieck trace formula, one may replace Z ` by any adic Z `-algebra, i.e. a compact, semilocal Z WebGrothendieck's Séminaire de géométrie algébrique; Grothendieck's six operations; Grothendieck's vanishing theorem; Grothendieck space; Grothendieck spectral sequence; Grothendieck–Springer resolution; Grothendieck–Teichmüller group; Grothendieck–Teichmüller theory; Grothendieck-Witt ring; Grothendieck trace …
Grothendieck trace formula over $\\mathbb{F}_{p^{n}}[[t]]$?
http://virtualmath1.stanford.edu/~conrad/Weil2seminar/Notes/L20.pdf WebDec 1, 2000 · This is the text of two lectures given at the Exponential Sums Conference held at The Hebrew University of Jerusalem in January 1998. In these lectures I reviewed some important results on exponential sums, which have been obtained by Deligne, Katz and others as consequences of the Grothendieck trace formula for the ℓ-adic cohomology … make your own computer software free
Perverse Sheaves and Fundamental Lemmas
WebLefschetz-Grothendieck trace formula, which counts the number of Fq-rational points of algebraic stacks. Fi-nally, we recall the zeta function for algebraic stacks and illustrate all the concepts for the fundamental example given by the multiplicative group scheme Gm. In the second section we calculate the rational ℓ-adic WebApr 11, 2024 · In algebraic geometry, Behrend's trace formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field conjectured in 1993 and proven in 2003 by Kai Behrend.Unlike the classical one, the formula counts points in the "stacky way"; it takes into account the presence of nontrivial … WebJan 5, 2012 · The aim of this short lecture course is to develop Selberg's trace formula for a compact hyperbolic surface M, and discuss some of its applications.The main motivation for our studies is quantum chaos: the Laplace-Beltrami operator –Δ on the surface M represents the quantum Hamiltonian of a particle, whose classical dynamics is governed by the … make your own concrete molds