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作者：Lin, Hsueh-Yung; Shinder, Evgeny
摘要：We construct invariants of birational maps with values in the Kontsevich- Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well -suited to investigating the structure of the Grothendieck ring and L -equivalence. Building on known constructions of L -equivalence, we prove new unexpected results about Cremona groups.
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作者：Cristofaro-Gardiner, Daniel; Humiliere, Vincent; Seyfaddini, Sobhan
摘要：In the 1970s, Fathi, having proven that the group of compactly supported volume -preserving homeomorphisms of the n -ball is simple for n >= 3, asked if the same statement holds in dimension two. We show that the group of compactly supported area -preserving homeomorphisms of the twodisc is not simple. This settles what is known as the simplicity conjecture in the affirmative. In fact, we prove the a priori stronger statement that this group is not perfect. Our general strategy is partially in...
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作者：Fu, Weibo
摘要：We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on SL2 over any number field that is not totally real. In particular, we establish a sharp bound on the growth of cuspidal Bianchi modular forms. We transfer our problem into a question over the completed universal enveloping algebras by applying an algebraic microlocalization of Ardakov and Wadsley to the completed homology. We prove finitely generated Iwasawa...
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作者：Baldi, Gregorio; Ullmo, Emmanuel
