Inventiones mathematicae

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• Algebraic Morava K-theories AI翻译
  作者：Borghesi, S
  作者单位：Universite Paris Saclay
  摘要：For any prime q and positive integer t, we construct a spectrum k(t) in the stable homotopy category of schemes over a field k equipped with an embedding k --> C. In classical homotopy theory, the C realization of k(t) is known as Morava K-theory. The algebraic content lies in the fact that these spectra are defined as the homotopy limit of a tower whose cofibers are appropriate suspensions of the motivic Eilenberg-MacLane spectra, which are known to represent motivic cohomology in the stable ...
• Toroidal varieties and the weak factorization theorem AI翻译
  作者：Wlodarczyk, J
  作者单位：Purdue University System; Purdue University
  摘要：We develop the theory of stratified toroidal varieties, which gives, together with the theory of birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blow-ups and blow-downs with smooth centers.
• Smooth points of T-stable varieties in G/B and the Peterson map AI翻译
  作者：Carrell, JB; Kuttler, J
  作者单位：University of British Columbia; University of Basel
  摘要：Let G be a connected semi-simple algebraic group defined over an algebraically closed field k, and let T subset of B subset of P be respectively a maximal torus, a Borel subgroup and a parabolic subgroup of G. Inspired by a beautiful result of Dale Peterson describing the singular locus of a Schubert variety in G/B, we characterize the T-fixed points in the singular locus of an arbitrary irreducible T-stable subvariety of G/P (a T-variety for short). Peterson's result (cf. The Deformation Theo...
• Cluster algebras II: Finite type classification AI翻译
  作者：Fomin, S; Zelevinsky, A
  作者单位：University of Michigan System; University of Michigan; Northeastern University
• Rational isomorphisms between K-theories and cohomology theories AI翻译
  作者：Friedlander, EM; Walker, ME
  作者单位：Northwestern University; University of Nebraska System; University of Nebraska Lincoln
  摘要：The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the Segre map) of infinite loop spaces. Moreover, the associated Chem character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced that establishes a useful general criterion for a natural transformation of functors on quasi-projective complex varieti...
• Scattering matrix in conformal geometry AI翻译
  作者：Graham, CR; Zworski, M
  作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
• Analytic continuation of holomorphic correspondences and equivalence of domains in Cn AI翻译
  作者：Shafikov, R
  作者单位：State University of New York (SUNY) System; Stony Brook University
  摘要：The following result is proved: Let D and D' be bounded domains in C-n, partial derivativeD is smooth, real-analytic, simply connected, and partial derivativeD' is connected, smooth, real-algebraic. Then there exists a proper holomorphic correspondence f : D --> D' if and only if there exist points p is an element of partial derivativeD and p' is an element of partial derivativeD', such that partial derivativeD and partial derivativeD' are locally CR-equivalent near p and p'. This leads to a c...
• Mirror symmetry, Langlands duality, and the Hitchin system AI翻译
  作者：Hausel, T; Thaddeus, M
  作者单位：University of California System; University of California Berkeley; Columbia University
  摘要：Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equa...
• Large deviation bounds for matrix Brownian motion AI翻译
  作者：Biane, P; Capitaine, M; Guionnet, A
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：We prove large deviation bounds for the convergence of Hermitian matrix valued Brownian motion towards free Brownian motion. As a consequence, we obtain upper and lower bounds on the microstates entropy introduced by Voiculescu [24].
• The cup product of Hilbert schemes for K3 surfaces AI翻译
  作者：Lehn, M; Sorger, C
  作者单位：Johannes Gutenberg University of Mainz; Nantes Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A([n]) so that there is canonical isomorphism of rings (H* (X; Q)[2])([n]) congruent to H* (X-[n]; Q)[2n] for the Hilbert scheme X-[n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.