Satake compactification
WebbA discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general ... De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern … WebbSatake compactifications A. Ash, D. Mumford, M. Rapoport, and Y. Tai, Smooth Compactifications of Locally Symmetric Varieties, Math. Sci. Press,... W. Baily and A. …
Satake compactification
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Webb2. The Baily Borel (Satake) compactification 2.1. The case G = SL(2). Recall the fundamental domains for the action of Γ = SL(2,Z) on the upper half plane h. 01234 Figure 1. Fundamental domains for SL(2,Z) The quotient X =Γ\h may be compactified, X = X ∪{∞}by adding a single cusp1 at infinity. If we wish to realize this as the Webb18 aug. 2015 · Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification Abbg of Ag stabilizes as g → ∞ and they computed this stable cohomology as a Hopf algebra.
Webb29 sep. 2024 · Arithmetic Satake compactifications and algebraic Drinfeld modular forms. In this article we construct the arithmetic Satake compactification of the Drinfeld moduli … Webb2. The Baily Borel (Satake) compactification 2.1. The case G = SL(2). Recall the fundamental domains for the action of Γ = SL(2,Z) on the upper half plane h. 01234 …
Webb21 apr. 2024 · A number of compactifications familiar in complex-analytic geometry, in particular the Baily–Borel compactification and its toroidal variants, as well as the Deligne–Mumford compactifications, can be covered by open subsets whose nonempty intersections are classified by their fundamental groups.We exploit this fact to define a … Webb1 juli 2024 · Satake compactification A type of compactification arising from work of I. Satake on the compactification of quotients of symmetric spaces by arithmetically …
WebbI. Satake, On the compactification of the Siegel space, J. Indian Math. Soc. 20 (1956) 259–281. Google Scholar; 20. I. Satake, Ĺopérateur ϕ, Séminaire Henri Cartan 10(2) (1957/58) 1–18. Google Scholar; 21. I. Satake, On compactifications of the quotient spaces for arithmetically defined discontinuous groups, Ann. of Math. 72(3) (1960 ...
Webb1 feb. 2024 · This generalizes work of Kapranov. Using an algebraic modular compactification that generalizes Pink and Schieder's, we show that the analytic … drawer will not stay shutWebbFor any measure γ on M we construct a map Ψγ from the Satake compactification of G/K (associated to V) to the Lie algebra of K. If γ is the K-invariant measure, then Ψγ is a homeomorphism of the Satake compactification onto the convex envelope of O. For a large class of measures the image of Ψγ is the convex envelope. drawer white bathroomWebb30 juli 2010 · We give an abstract characterization of the Satake compactification of a general Drinfeld modular variety. We prove that it exists and is unique up to unique isomorphism, though we do not give an explicit stratification by Drinfeld modular varieties of smaller rank which is also expected. drawer wine coolerWebbRecall Berkovich gave a compactification of Bruhat-Tits building B(G, k) for semisimple algebraic group G over non-archimedean field i.e., closure inside the analytification of flag variety along ... employees provident funds schemeWebb6 apr. 2002 · The cohomology of A 3 and its Satake compactification was computed by Hain [Hai02], the Chow ring of A 3 and its toroidal compactification was computed by van der Geer [vdG98], and the second ... drawer wine glass storageWebb17 okt. 2024 · Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen type. We provide a moduli-theoretic framework for the collapsing … employeesql githubWebbHere, the left-hand side is the Lpsuperscript𝐿𝑝L^{p}italic_L start_POSTSUPERSCRIPT italic_p end_POSTSUPERSCRIPT-cohomology of M𝑀Mitalic_M with respect to a (locally) inva drawer with closet