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作者：Bhattacharya, Prasit; Kitchloo, Nitu
摘要：In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the K-theory functor to a multinatural transformation. We also point out that the original proof of the stable Adams conjecture is incorrect and present a correction. This correction is crucial to our main application. We settle the question on the height of higher associative structures on the mod...
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作者：Buzzi, Jerome; Crovisier, Sylvain; Sarig, Omri
摘要：We show that C-infinity-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irred...
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
摘要：In this paper and its sequel, we construct a set of finite energy smooth initial data for which the corresponding solutions to the compressible three-dimensional Navier-Stokes and Euler equations implode (with infinite density) at a later time at a point, and we completely describe the associated formation of singularity. This paper is concerned with existence of smooth self-similar profiles for the barotropic Euler equations in dimension d >= 2 with decaying density at spatial infinity. The p...
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作者：Wang, Qian
摘要：We prove the local-in-time well-posedness for the solution of the compressible Euler equations in 3-D for the Cauchy data of the velocity, density and vorticity (upsilon, rho, w) is an element of H-s x H-s x H-s('), 2 < s' < s. The result extends the sharp results of Smith-Tataru and of Wang, established in the irrotational case, i.e., w = 0, which is known to be optimal for s > 2. At the opposite extreme, in the incompressible case, i.e., with a constant density, the result is known to hold f...
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作者：Liu, Yuchen; Xu, Chenyang; Zhuang, Ziquan
摘要：We prove that on any log Fano pair of dimension n whose stability threshold is less than n+1/n, any valuation computing the stability threshold has a finitely generated associated graded ring. Together with earlier works, this implies that (a) a log Fano pair is uniformly K-stable (resp. reduced uniformly K-stable) if and only if it is K-stable (resp. K-polystable); (b) the K-moduli spaces are proper and projective; and combining with the previously known equivalence between the existence of K...
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作者：Sawin, Will; Shusterman, Mark
摘要：Using geometric methods, we improve on the function field version of the Burgess bound and show that, when restricted to certain special subspaces, the Mobius function over F-q[T] can be mimicked by Dirichlet characters. Combining these, we obtain a level of distribution close to 1 for the Mobius function in arithmetic progressions and resolve Chowla's k-point correlation conjecture with large uniformity in the shifts. Using a function field variant of a result by Fouvry-Michel on exponential ...
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作者：Witaszek, Jakub
摘要：We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel's base point free theorem obtaining applications towards the mixed characteristic Minimal Model Program, we generalise Kollar's theorem on the existence of quotients by finite equivalence relations to mixed characteristic, and we provide a new proof of the existence of quotients by affine group schemes.
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
摘要：In this paper, which continues our investigation of strong singularity formation in compressible fluids, we consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is...
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作者：Bachmann, Tom; Kong, Hana Jia; Wang, Guozhen; Xu, Zhouli
摘要：We define the Chow t-structure on the infinity-category of motivic spectra SH(k) over an arbitrary base field k. We identify the heart of this t-structure SH(k)(c(sic)) when the exponential characteristic of k is inverted. Restricting to the cellular subcategory, we identify the Chow heart SH(k)(cell,c(sic)) as the category of even graded MU2*MU-comodules. Furthermore, we show that the co-category of modules over the Chow truncated sphere spectrum 1(c=0) is algebraic. Our results generalize th...
