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Crystalline Cohomology Of Algebraic Stacks And Hyodo Kato Cohomology
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Book Synopsis Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology by : Martin C. Olsson
Download or read book Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology written by Martin C. Olsson and published by . This book was released on 2007 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Notes on Crystalline Cohomology. (MN-21) by : Pierre Berthelot
Download or read book Notes on Crystalline Cohomology. (MN-21) written by Pierre Berthelot and published by Princeton University Press. This book was released on 2015-03-08 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Universal Extensions and One Dimensional Crystalline Cohomology by : B. Mazur
Download or read book Universal Extensions and One Dimensional Crystalline Cohomology written by B. Mazur and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Book Synopsis Algebraic Geometry by : Dan Abramovich
Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Local Cohomology Sheaves on Algebraic Stacks by : Tobias Sitte
Download or read book Local Cohomology Sheaves on Algebraic Stacks written by Tobias Sitte and published by . This book was released on 2014 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rigid Cohomology for Algebraic Stacks by : David Brown
Download or read book Rigid Cohomology for Algebraic Stacks written by David Brown and published by . This book was released on 2010 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend le Stum's construction of the overconvergent site to algebraic stacks. We prove that etale morphisms are morphisms of cohomological descent for finitely presnted crystals on the overconvergent site. Finally, using the notion of an open subtopos of SGA4, we define a notion of overconvergent cohomology supported in a closed substack and show that it agrees with the classical notion of rigid cohomology supported in a closed subscheme.
Book Synopsis Universal Extensions and One Dimensional Crystalline Cohomology by : B Mazur
Download or read book Universal Extensions and One Dimensional Crystalline Cohomology written by B Mazur and published by . This book was released on 2014-01-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cycle Classes for Algebraic De Rham Cohomology and Crystalline Cohomology by : Nicholas Ring
Download or read book Cycle Classes for Algebraic De Rham Cohomology and Crystalline Cohomology written by Nicholas Ring and published by . This book was released on 2002 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bergman Kernels and Symplectic Reduction by : Xiaonan Ma
Download or read book Bergman Kernels and Symplectic Reduction written by Xiaonan Ma and published by . This book was released on 2008 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diffraction of Singularities for the Wave Equation on Manifolds with Corners by : Richard B. Melrose
Download or read book Diffraction of Singularities for the Wave Equation on Manifolds with Corners written by Richard B. Melrose and published by . This book was released on 2013 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Real and Etale Cohomology by : Claus Scheiderer
Download or read book Real and Etale Cohomology written by Claus Scheiderer and published by Lecture Notes in Mathematics. This book was released on 1994-10-27 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.
Book Synopsis Universal Extensions and One Dimensional Crystalline Cohomology by : Barry Mazur
Download or read book Universal Extensions and One Dimensional Crystalline Cohomology written by Barry Mazur and published by . This book was released on 1974 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cohomological Theory of Crystals Over Function Fields by : Gebhard Böckle
Download or read book Cohomological Theory of Crystals Over Function Fields written by Gebhard Böckle and published by European Mathematical Society. This book was released on 2009 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a new cohomological theory for schemes in positive characteristic $p$ and it applies this theory to give a purely algebraic proof of a conjecture of Goss on the rationality of certain $L$-functions arising in the arithmetic of function fields. These $L$-functions are power series over a certain ring $A$, associated to any family of Drinfeld $A$-modules or, more generally, of $A$-motives on a variety of finite type over the finite field $\mathbb{F}_p$. By analogy to the Weil conjecture, Goss conjectured that these $L$-functions are in fact rational functions. In 1996 Taguchi and Wan gave a first proof of Goss's conjecture by analytic methods a la Dwork. The present text introduces $A$-crystals, which can be viewed as generalizations of families of $A$-motives, and studies their cohomology. While $A$-crystals are defined in terms of coherent sheaves together with a Frobenius map, in many ways they actually behave like constructible etale sheaves. A central result is a Lefschetz trace formula for $L$-functions of $A$-crystals, from which the rationality of these $L$-functions is immediate. Beyond its application to Goss's $L$-functions, the theory of $A$-crystals is closely related to the work of Emerton and Kisin on unit root $F$-crystals, and it is essential in an Eichler - Shimura type isomorphism for Drinfeld modular forms as constructed by the first author. The book is intended for researchers and advanced graduate students interested in the arithmetic of function fields and/or cohomology theories for varieties in positive characteristic. It assumes a good working knowledge in algebraic geometry as well as familiarity with homological algebra and derived categories, as provided by standard textbooks. Beyond that the presentation is largely self contained.
Book Synopsis Comparison of Relatively Unipotent Log de Rham Fundamental Groups by : Bruno Chiarellotto
Download or read book Comparison of Relatively Unipotent Log de Rham Fundamental Groups written by Bruno Chiarellotto and published by American Mathematical Society. This book was released on 2023-09-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Logarithmic Algebraic Geometry by : Arthur Ogus
Download or read book Lectures on Logarithmic Algebraic Geometry written by Arthur Ogus and published by Cambridge University Press. This book was released on 2018-11-08 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Book Synopsis Revisiting the de Rham-Witt Complex by : Bhargav Bhatt
Download or read book Revisiting the de Rham-Witt Complex written by Bhargav Bhatt and published by . This book was released on 2021 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
