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Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case

2011-02-07 Mathematics
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Release : 2011-02-07
Genre : Mathematics
Kind : eBook
Book Rating : 40X/5 ( reviews)

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Book Synopsis Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case by : Martin C. Olsson

Download or read book Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case written by Martin C. Olsson. This book was released on 2011-02-07. Available in PDF, EPUB and Kindle. Book excerpt: 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

2023-03-28 Mathematics
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Release : 2023-03-28
Genre : Mathematics
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Book Rating : 508/5 ( reviews)

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Book Synopsis p-adic Hodge Theory, Singular Varieties, and Non-Abelian Aspects by : Bhargav Bhatt

Download or read book p-adic Hodge Theory, Singular Varieties, and Non-Abelian Aspects written by Bhargav Bhatt. This book was released on 2023-03-28. Available in PDF, EPUB and Kindle. Book excerpt: 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

2016-09-06 Mathematics
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Release : 2016-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 815/5 ( reviews)

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Book Synopsis Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting by : J. P. Pridham

Download or read book Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting written by J. P. Pridham. This book was released on 2016-09-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

2011 Mathematics
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Release : 2011
Genre : Mathematics
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Book Rating : 388/5 ( reviews)

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Book Synopsis Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates by : Steve Hofmann

Download or read book Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates written by Steve Hofmann. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: 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$_2$

2012-02-22 Mathematics
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Release : 2012-02-22
Genre : Mathematics
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Book Rating : 272/5 ( reviews)

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Book Synopsis Towards a Modulo $p$ Langlands Correspondence for GL$_2$ by : Christophe Breuil

Download or read book Towards a Modulo $p$ Langlands Correspondence for GL$_2$ written by Christophe Breuil. This book was released on 2012-02-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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