Annals of Mathematics

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• Ramification theory for varieties over a perfect field AI翻译
  作者：Kato, Kazuya; Saito, Takeshi
  摘要：For an l-adic sheaf on a variety of arbitrary dimension over a perfect field, we define the Swan class measuring the wild ramification as a 0-cycle class supported on the ramification locus. We prove a Lefschetz trace formula for open varieties and a. generalization of the Grothendieck-Ogg-Shararevich formula using the Swan class.
• Maharam's problem AI翻译
  作者：Talagrand, Michel
  摘要：We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947).
• Fundamental lemma for unitary groups AI翻译
  作者：Laumon, Gerard; Ngo, Bao Chau
  摘要：Let G be an unramified reductive group over a nonarchimedian local field F. The so-called Langlands Fundamental Lemma is a family of conjectural identities between orbital integrals for G(F) and orbital integrals for endoscopic groups of G. In this paper we prove the Langlands fundamental lemma in the particular case where F is a finite extension of Fp((t)), G is a unitary group and p > rank(G). Waldspurger has shown that this particular case implies the Langlands fundamental lemma for unitary...
• The strong Macdonald conjecture and Hodge theory on the loop Grassmannian AI翻译
  作者：Fishel, Susanna; Grojnowski, Ian; Teleman, Constantin
  摘要：We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a. geometric reformulation, we show that the Dolbeault cohomology H-q(X; Omega(p)) of the loop Grassmannian X is freely generated by de Rham's forms on the disk coupled to the indecomposables of H degrees(BG). Equating the two Euler characteristics gives an identity, independently known to Macdonald [M], which generalises Ramanujan's 1 psi 1 sum. For simply laced root systems at level I., we also find a. '...
• On the zeros of cosine polynomials: solution to a problem of Littlewood AI翻译
  作者：Borwein, P.; Erdelyi, T.; Ferguson, R.; Lockhart, R.
  摘要：Littlewood in his 1968 monograph Some Problems in Real and Complex Analysis [12, Problem 22] poses the following research problem, which appears to be still open: PROBLEM. If the n(j) are integral and all different, what is the lower bound on the number of real zeros of Sigma(N)(j=1) COS(n(j)theta)? Possibly N-1, or not much less. No progress seems to have been made on this in the last half century. We show that this is false. THEOREM. There exists a cosine polynomial Sigma(N)(j=1) COS(n(j)the...
• On the homology of algebras of Whitney functions over subanalytic sets AI翻译
  作者：Brasselet, Jean-Paul; Pflaum, Markus J.
  摘要：In this article we study several homology theories of the algebra epsilon(infinity)(X) of Whitney functions over a subanalytic set X subset of R-n with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for epsilon(infinity)(X), when X is a regular subset of R-n having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of epsilon(infinity)(X)...
• On Mott's formula for the ac-conductivity in the Anderson model AI翻译
  作者：Klein, Abel; Lenoble, Olivier; Mueller, Peter
  摘要：We study the ac-conductivity in linear response theory in the general framework of ergodic magnetic Schrodinger operators. For the Anderson model, if the Fermi energy lies in the localization regime, we prove that the ac-conductivity is bounded from above by Cv(2)(log1/v)(d+2) at small frequencies v. This is to be compared to Mott's formula, which predicts the leading term to be Cv(2)(log1/v)(d+1).
• Weyl group multiple Dirichlet series III:: Eisenstein series and twisted unstable Ar AI翻译
  作者：Brubaker, B.; Bump, D.; Friedberg, S.; Hoffstein, J.
  摘要：Weyl group multiple Dirichlet series were associated with a root system Phi and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker, Bump and Friedberg [4] provided n is sufficiently large; their coefficients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when Phi = A(r). Twisted Dirichet series are considered, which contain the series of [4] as a special case. These series a...
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics AI翻译
  作者：Cao, Chongsheng; Titi, Edriss S.
  摘要：In this paper we prove the global existence and uniqueness (regularity) of strong solutions to the three-dimensional viscous primitive equations, which model large scale ocean and atmosphere dynamics.
• On the K2 of degenerations of surfaces and the multiple point formula AI翻译
  作者：Calabri, A.; Ciliberto, C.; Flamini, F.; Miranda, R.
  摘要：In this paper we study some properties of reducible surfaces, in particular of unions of planes. When the surface is the central fibre of an embedded flat degeneration of surfaces in a projective space, we deduce some properties of the smooth surface which is the general fibre of the degeneration from some combinatorial properties of the central fibre. In particular, we show that there are strong constraints on the invariants of a smooth surface which degenerates to configurations of planes wi...