Towards Non Abelian P Adic Hodge Theory In The Good Reduction Case

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Towards Non Abelian P Adic Hodge Theory In The Good Reduction Case

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Author : Martin C. Olsson
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-02-07

Towards Non Abelian P Adic Hodge Theory In The Good Reduction Case written by Martin C. Olsson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-07 with Mathematics categories.

The author develops a non-abelian version of $p$-adic Hodge Theory for varieties (possibly open with ``nice compactification'') with good reduction. This theory yields in particular a comparison between smooth $p$-adic sheaves and $F$-isocrystals on the level of certain Tannakian categories, $p$-adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups.

P Adic Hodge Theory Singular Varieties And Non Abelian Aspects

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Author : Bhargav Bhatt
language : en
Publisher: Springer Nature
Release Date : 2023-03-28

P Adic Hodge Theory Singular Varieties And Non Abelian Aspects written by Bhargav Bhatt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-28 with Mathematics categories.

This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.

Real Non Abelian Mixed Hodge Structures For Quasi Projective Varieties Formality And Splitting

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Author : J. P. Pridham
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-06

Real Non Abelian Mixed Hodge Structures For Quasi Projective Varieties Formality And Splitting written by J. P. Pridham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.

The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x−i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.

Hardy Spaces Associated To Non Negative Self Adjoint Operators Satisfying Davies Gaffney Estimates

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Author : Steve Hofmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Hardy Spaces Associated To Non Negative Self Adjoint Operators Satisfying Davies Gaffney Estimates written by Steve Hofmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.

Towards A Modulo P Langlands Correspondence For Gl 2

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Author : Christophe Breuil
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-02-22

Towards A Modulo P Langlands Correspondence For Gl 2 written by Christophe Breuil and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-22 with Mathematics categories.

The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.

The Motivic Anabelian Geometry Of Local Heights On Abelian Varieties

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Author : L. Alexander Betts
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13

The Motivic Anabelian Geometry Of Local Heights On Abelian Varieties written by L. Alexander Betts and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-13 with Mathematics categories.

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Algebraic Geometry

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Author : Dan Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Algebraic Geometry written by Dan Abramovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

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.

A Von Neumann Algebra Approach To Quantum Metrics Quantum Relations

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Author : Greg Kuperberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

A Von Neumann Algebra Approach To Quantum Metrics Quantum Relations written by Greg Kuperberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.

Second Order Analysis On Mathscr P 2 M W 2

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Author : Nicola Gigli
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-02-22

Second Order Analysis On Mathscr P 2 M W 2 written by Nicola Gigli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-22 with Mathematics categories.

The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.

Positive Definiteness Of Functions With Applications To Operator Norm Inequalities

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Author : Hideki Kosaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-06-10

Positive Definiteness Of Functions With Applications To Operator Norm Inequalities written by Hideki Kosaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-10 with Mathematics categories.

Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.