9/24/2023 0 Comments Semi stacks![]() ![]() Jacquet, H., Lapid, E., Rogawski, J.: Periods of automorphic forms. ![]() Jacquet, H.: Sur un résultat de Waldspurger. arXiv:1410.0435īernstein, J., Krötz, B.: Smooth Fréchet globalizations of Harish–Chandra modules. What is a continuous representation of an algebraic group? Preprint. īernstein, J.: Stacks in representation theory. arXiv:1502.03528v2īaruch, E.M.: A proof of Kirillov’s conjecture. doi: 10.1017/CBO9780511674693Ītobe, H.: The local theta correspondence and the local Gan–Gross–Prasad conjecture for the symplectic-metaplectic case. With the collaboration of Peter Scholze (2010). doi: 10.2307/1990948Īsh, A., Mumford, D., Rapoport, M., Tai, Y.-S.: Smooth Compactifications of Locally Symmetric Varieties, 2nd edn. doi: 10.1353/ajm.2013.0000Īlper, J.: On the local quotient structure of Artin stacks. doi: 10.1007/s1185-9Īizenbud, A., Gourevitch, D.: Smooth transfer of Kloosterman integrals (the Archimedean case). doi: 10.1093/imrn/rnm155Īizenbud, A., Gourevitch, D.: The de-Rham theorem and Shapiro lemma for Schwartz function on Nash manifolds. In any case, the stack-theoretic point of view provides an explanation for the pure inner forms that appear in many versions of the Langlands, and relative Langlands, conjectures.Īizenbud, A., Gourevitch, D.: Schwartz functions on Nash manifolds. These evaluation maps produce, in principle, a distribution which generalizes the Arthur–Selberg trace formula and Jacquet’s relative trace formula, although the former, and many instances of the latter, cannot actually be defined by the purely geometric methods of this paper. This corresponds to a regularization of the sum of those orbital integrals whose semisimple part corresponds to the chosen k-point. Moreover, when those are obtained from algebraic quotient stacks of the form X/ G, with X a smooth affine variety and G a reductive group defined over a number field k, we define, whenever possible, an “evaluation map” at each semisimple k-point of the stack, without using truncation methods. We extend this definition to smooth semi-algebraic stacks, which are defined as geometric stacks in the category of Nash manifolds. Schwartz functions, or measures, are defined on any smooth semi-algebraic (“Nash”) manifold, and are known to form a cosheaf for the semi-algebraic restricted topology. ![]()
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