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作者：Yuan, Xinyi
作者单位：Peking University
摘要：In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties r...
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作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
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作者：Yuan, Xinyi
作者单位：Peking University
摘要：In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties r...
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作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
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作者：Newton, James; Thorne, Jack
作者单位：University of Oxford; University of Cambridge
摘要：Let F be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of GL2(AF) associated to Hilbert modular forms of regular weight.
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作者：Berger, Pierre
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points that are not conjugate to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen to be ergodic or, to the contrary, with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solves a problem of Herman (1998). One aspect of the proof provides a new approximation theorem; it enables the implementation ...
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作者：Pan, Lue
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：This is a continuation of our previous work on the locally analytic vectors of the completed cohomology of modular curves. We construct differential operators on modular curves with infinite level at p in both holomorphic and anti-holomorphic directions. As applications, we reprove a classicality result of Emerton which says that every absolutely irreducible two dimensional Galois representation that is regular de Rham at p and appears in the completed cohomology of modular curves comes from a...
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作者：Burungale, Ashay A.; Tian, Ye
作者单位：California Institute of Technology; University of Texas System; University of Texas Austin; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：Let E be a CM elliptic curve defined over Q and p a prime. We show that corankZp Selp infinity (E/Q) = 0 =double right arrow ords=1L(s, E/Q) = 0 for the p infinity- Selmer group Selp infinity(E/Q) and the complex L-function L(s, E/Q). Along with Smith's work on the distribution of 2 infinity-Selmer groups, this leads to the first instance of the even parity Goldfeld conjecture: For 50% of the positive square-free integers n, we have ords=1L(s, E/Q(n)) = 0, where E(n) : ny2 = x3-x is a quadrati...
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作者：Giri, Vikram; Kwon, Hyunju; Novack, Matthew
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; Purdue University System; Purdue University
摘要：In this work, we prove the L-3-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to C-t(0)(W-1/3-,W-3 boolean AND L infinity-). More precisely, for every beta < 1/3, we can construct such solutions in the space C-t(0)(B-3,infinity(beta) boolean AND 1/L1-3 beta).
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作者：Calmes, Baptiste; Dotto, Emanuele; Harpaz, Yonatan; Hebestreit, Fabian; Land, Markus; Moi, Kristian; Nardin, Denis; Nikolaus, Thomas; Steimle, Wolfgang
作者单位：Universite d'Artois; University of Warwick; Sorbonne Universite; Universite Paris Cite; University of Bielefeld; Johannes Gutenberg University of Mainz; Royal Institute of Technology; University of Regensburg; University of Munster; University of Augsburg
摘要：We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring R to the homotopy C-2-orbits of its K-theory and Ranicki's original (non-periodic) symmetric L-theory. We use this fibre sequence to remove the assumption that 2 is a unit in R from various results about Grothendieck-Witt groups. For instance, we solve the homotopy limit problem for Dedekind rings whose fraction field is a number field, calculate the various flavours of Grothendieck-Witt groups of Z, show t...
