Integral $p$-adic Hodge theory — announcement
نویسندگان
چکیده
منابع مشابه
Relative p-adic Hodge theory, I: Foundations
We initiate a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of Berkovich. In this paper, we give a thorough development of φ-modules over a relative Robba ring associated to a perfect Banach ring of characteristic p, including the relationship between these objects and étale Zp-local systems an...
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3 Construction of BdR 4 3.1 Witt Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Lifting to a Perfect Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Carrying Out the Lifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.4 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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Stringy Hodge numbers are introduced by Batyrev for a mathematical formulation of mirror symmetry. However, since the stringy Hodge numbers of an algebraic variety are defined by choosing a resolution of singularities, the well-definedness is not clear from the definition. Batyrev proved the well-definedness by using the theory of motivic integration developed by Kontsevich, Denef-Loeser. The a...
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In this article, we study integral structures on p-adic Fourier theory by Schneider and Teitelbaum. As an application of our result, we give a certain integral basis of the space of K-locally analytic functions for any finite extension K of Qp, generalizing the basis of Amice of locally analytic functions on Zp. We also use our result to prove congruences of Bernoulli-Hurwitz numbers at supersi...
متن کاملSome new directions in p-adic Hodge theory
We recall some basic constructions from p-adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B-pairs, introduced recently by Berger, which provides a natural enlargement of the category of p-adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representati...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2015
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2015.v22.n6.a3