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Concept

Motive (algebraic geometry)

Related publications (24)

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

Lamplighters and the bounded cohomology of Thompson's group

Nicolas Monod

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range of coefficients. This implies the same vanishing for a number of groups with self-similarity properties, such as Thompson's group F. In particular, these groups are bou ...

SPRINGER BASEL AG2022

Unramified F-divided objects and the etale fundamental pro-groupoid in positive characteristic

Giulio Orecchia

Let X /S be a flat algebraic stack of finite presentation. We define a new & eacute;tale fundamental pro-groupoid pi(1)(X /S), generalizing Grothendieck's enlarged & eacute;tale fundamental group from SGA 3 to the relative situation. When S is of equal pos ...

GEOMETRY & TOPOLOGY PUBLICATIONS2022

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

Algebraic Homotopy Interleaving Distance

Nicolas Michel Berkouk

The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

2021

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...

OXFORD UNIV PRESS2019

Simple and projective correspondence functors

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...

2021

The cup product of Brooks quasimorphisms

Nicolas Monod

We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups. ...

WALTER DE GRUYTER GMBH2018

Relative Homological Algebra Via Truncations

Jérôme Scherer

To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spal-tenstein solved this problem for chain complexes of R-modules by truncating further and further to the left, resolving the pieces, and ...

FIZ KARLSRUHE-LEIBNIZ-INST INFORMATIONSINFRASTRUKTUR2018

Motivic and p-adic Localization Phenomena

Dimitri Stelio Wyss

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the

p

-adic pushforward of the Haar measure under a ...

EPFL2017

L-2-Betti Numbers Of Rigid C*-Tensor Categories And Discrete Quantum Groups

Sven Raum

We compute the L-2-Betti numbers of the free C*-tensor categories, which are the representation categories of the universal unitary quantum groups A(u)(F). We show that the L-2-Betti numbers of the dual of a compact quantum group G are equal to the L-2-Bet ...

Mathematical Science Publ2017

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

The homotopy theory of coalgebras over a comonad

Kathryn Hess Bellwald

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...

2014

L-2-Betti numbers and Plancherel measure

Henrik Densing Petersen

We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...

Academic Press Inc Elsevier Science2014

Injective Classes of Modules

Jérôme Scherer

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisel ...

2013

L-2-Betti numbers of locally compact groups

Henrik Densing Petersen

The present paper is a summary and overview of results obtained in the author's thesis, "L-2-Betti Numbers of Locally Compact Groups", wherein the definition of L-2-Betti numbers for countable groups is extended to locally compact unimodular groups. In man ...

Elsevier2013

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

Generalized tensor idempotents and the telescope conjecture

Giordano Favi

We transpose Rickard's construction of idempotent representations to the general context of tensor triangulated categories. We connect our construction to the telescope conjecture and prove that the latter is of local nature. As an illustration, we extend ...

2011

Related publications (24)

p

-adic pushforward of the Haar measure under a ...

EPFL2017

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

Generalized tensor idempotents and the telescope conjecture

Giordano Favi

2011