Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology PDF Download
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Author: Martin C. Olsson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 422
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Book Description
In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a $p$-adic field and applications to $p$-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of $p$-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
Author: Martin C. Olsson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 422
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Book Description
In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a $p$-adic field and applications to $p$-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of $p$-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
Author: Dan Abramovich
Publisher: American Mathematical Soc.
ISBN: 0821847031
Category : Mathematics
Languages : en
Pages : 539
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Book Description
Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.
Author: B. Mazur
Publisher: Springer
ISBN: 3540379339
Category : Mathematics
Languages : en
Pages : 142
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Book Description
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Author: Xiaonan Ma
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 172
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Book Description
The authors generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property. More precisely, they study the asymptotic expansion of the $G$-invariant Bergman kernel of the $\mathrm{spin}^c$ Dirac operator associated with high tensor powers of a positive line bundle on a symplectic manifold admitting a Hamiltonian action of a compact connected Lie group $G$. The authors also develop a way to compute the coefficients of the expansion, and compute the first few of them; especially, they obtain the scalar curvature of the reduction space from the $G$-invariant Bergman kernel on the total space. These results generalize the corresponding results in the non-equivariant setting, which have played a crucial role in the recent work of Donaldson on stability of projective manifolds, to the geometric quantization setting. As another kind of application, the authors establish some Toeplitz operator type properties in semi-classical analysis in the framework of geometric quantization. The method used is inspired by Local Index Theory, especially by the analytic localization techniques developed by Bismut and Lebeau.
Author: Richard B. Melrose
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 148
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Book Description
The authors consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, the authors show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, the authors show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend the authors' previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.
Author: Bruno Chiarellotto
Publisher: American Mathematical Society
ISBN: 1470467062
Category : Mathematics
Languages : en
Pages : 124
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Book Description
View the abstract.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1596
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Book Description
Author: Arthur Ogus
Publisher: Cambridge University Press
ISBN: 1107187737
Category : Mathematics
Languages : en
Pages : 559
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Book Description
A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Author: Bhargav Bhatt
Publisher:
ISBN: 9782856299371
Category :
Languages : en
Pages : 165
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Book Description
Author: Chris A.M. Peters
Publisher: Springer Science & Business Media
ISBN: 3540770178
Category : Mathematics
Languages : en
Pages : 467
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Book Description
This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.
