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Correspondence functors and finiteness conditions

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A counterexample to the local-global principle of linear dependence for Abelian varieties

Antonella Perucca, Peter Simon Jossen

Let A be an Abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) f ...

2010

Tuning Mechanisms in Optofluidics

Demetri Psaltis, Wuzhou Song, Jae-Woo Choi

Novel functionalities have been developed through the fusion of optics and microfluidics. We categorize the different possible tuning mechanisms in optofluidics and describe the recent examples in each category. (C)2010 Optical Society of America ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Optically Generated Electric Fields by Lithium Niobate Nanowires

Demetri Psaltis, László Forró, Arnaud Magrez, Ye Pu, Rachel Grange, Chia-Lung Hsieh, Jae-Woo Choi, Rita Smajda

We demonstrate that lithium niobate nanowires generate electric fields under 514 nm continuous wave laser illumination. Birefringent media are used to visualize the generated fields in a microfluidic channel. Input laser polarization dependence is shown. ( ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Jean Fasel

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d

2009

Separation and Duality in Locally L0-Convex Modules

Damir Filipovic

Motivated by financial applications, we study convex analysis for modules over the ordered ring L0 of random variables. We establish a module analogue of locally convex vector spaces, namely locally L0-convex modules. In this context, we prove hyperplane s ...

2009

Convexly independent subsets of the Minkowski sum of planar point sets

János Pach, Friedrich Eisenbrand, Thomas Rothvoss

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P⊕Q which consist of convex independent points. We show that, if P and Q contain at most n points, then |S| = O(n^(4/3) ...

American Mathematical Society2008

A vanishing theorem for oriented intersection multiplicities

Jean Fasel

Let A be a regular local ring containing 1/2, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of A satisfy the following property: given two elements ...

2008

Varieties of modules for Z/2Z x Z/2Z

Let k be an algebraically closed field of characteristic 2. We prove that the restricted nilpotent commuting variety C, that is the set of pairs of (n x n)-matrices (A, B) such that A(2) = B-2 = [A, B] = 0, is equidimensional. C can be identified with the ...

Elsevier2007

Generic representations of orthogonal groups: the mixed functors

Christine Vespa

In previous work, we defined the category of functors F-quad, associated to F-2-vector spaces equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category F-quad, named the mixed functors. We give the c ...

2007

Modules d'endo-p-permutation

Jean-Marie Urfer

This dissertation is concerned with the study of a new family of representations of finite groups, the endo-p-permutation modules. Given a prime number p, a finite group G of order divisible by p and an algebraically closed field k of characteristic p, we ...

EPFL2006