Publications related to Exterior algebra

Multigraded algebras and multigraded linear series

Leonid Monin, Fatemeh Mohammadi, Yairon Cid Ruiz

This paper is devoted to the study of multigraded algebras and multigraded linear series. For an Ns

\mathbb {N}s

-graded algebra A

A

, we define and study its volume function FA:N+s -> R

F_A:\mathbb {N}_+s\rightarrow \mathbb {R}

, which computes the ...

Wiley2024

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

Zsolt Patakfalvi, Joseph Allen Waldron

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F-regularity to mixed characteristic and identify certain stable sections of adjoint lin ...

SPRINGER HEIDELBERG2023

On the Grothendieck-Serre conjecture for classical groups

Eva Bayer Fluckiger

We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...

WILEY2022

Conjugation spaces are cohomologically pure

Jérôme Scherer

Conjugation spaces are equipped with an involution such that the fixed points have the same mod 2 cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by 2, generalizing the classical examples of complex ...

WILEY2021

Realizing doubles: a conjugation zoo

Jérôme Scherer

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

CAMBRIDGE UNIV PRESS2021

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

Let A be a nonnegatively graded connected algebra over a noncommutative separable k-algebra K, and let M be a bounded below graded right A-module. If we denote by T the -coalgebra , we know that there exists an -comodule structure on over T. The structure ...

2019

Multisensory perceptual awareness: Categorical or graded?

Olaf Blanke, Nathan Quentin Faivre, Jean-Paul Noel

Neural evidence suggests that mechanisms associated with conscious access (i.e., the ability to report on a conscious state) are “all-or-none”. Upon crossing some threshold, neural signals are globally broadcast throughout the brain and allow conscious rep ...

2019

A higher homotopic extension of persistent (co)homology

Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in induces a multiplicative filtration on the dg algebra of simplicial cochains, w ...

2018

Depth-dependent mechanical properties of human articular cartilage obtained by indentation measurements

Pierre-Etienne Bourban, Lee Ann Laurent-Applegate, Robin Martin, Matteo Gregorio Modesto Marascio, Jens Antons

Emerging 3D printing technology permits innovative approaches to manufacture cartilage scaffolds associated with layer-by-layer mechanical property adaptation. However, information about gradients of mechanical properties in human articular cartilage is li ...

2018

Spectral sequences associated to deformations

Lapin has constructed a multiplicative spectral sequence from a deformation of an -algebra. In particular, as noted by the same author, one can apply this construction to a deformation induced by a filtration of an -algebra. A question that naturally appea ...

2017

Exterior algebra

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Multigraded algebras and multigraded linear series

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

On the Grothendieck-Serre conjecture for classical groups

Conjugation spaces are cohomologically pure

Realizing doubles: a conjugation zoo

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

Multisensory perceptual awareness: Categorical or graded?

A higher homotopic extension of persistent (co)homology

Depth-dependent mechanical properties of human articular cartilage obtained by indentation measurements

Spectral sequences associated to deformations

Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups

On the Grothendieck-Serre conjecture for classical groups

Spectral sequences associated to deformations

Multigraded algebras and multigraded linear series

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

A higher homotopic extension of persistent (co)homology

Realizing doubles: a conjugation zoo

Depth-dependent mechanical properties of human articular cartilage obtained by indentation measurements

Conjugation spaces are cohomologically pure

Multisensory perceptual awareness: Categorical or graded?