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In \textit{Shimuravariet\"{a}ten und Gerben} \cite{LR87}, Langlands and Rapoport developed the theory of pseudo-motivic Galois gerb and admissible morphisms between Galois gerbs, with a view to formulating a conjectural description of the…

Number Theory · Mathematics 2016-03-16 Dong Uk Lee

We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces,…

Group Theory · Mathematics 2013-01-07 Werner Hoffmann

Let $p$ be a prime number and let $k\geq 2$ be an integer. In this article we study the semi-simple reductions modulo $p$ of two-dimensional irreducible crystalline $p$-adic Galois representations with Hodge-Tate weights $0$ and $k-1$ and…

Number Theory · Mathematics 2021-03-09 Bodan Arsovski

We prove, using invariant Zariski-Riemann spaces, that every normal toric variety over a valuation ring of rank one can be embedded as an open dense subset into a proper toric variety equivariantly. This extends a well known theorem of…

Algebraic Geometry · Mathematics 2017-04-07 Alejandro Soto

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the…

Machine Learning · Statistics 2026-04-08 Huan Qing

P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…

Commutative Algebra · Mathematics 2016-01-25 Zaqueu Ramos , Aron Simis

There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing…

Category Theory · Mathematics 2015-11-20 Joseph Lipman

In this article, we use the Combinatorial Nullstellensatz to give new proofs of the Cauchy-Davenport, the Dias da Silva-Hamidoune and to generalize a previous addition theorem of the author. Precisely, this last result proves that for a set…

Combinatorics · Mathematics 2017-02-22 Eric Balandraud

Hara and Yoshida introduced a notion of $\aaa$-tight closure in 2003, and they proved that the test ideals given by this operation correspond to multiplier ideals. However, their operation is not a true closure. The alternative operation…

Commutative Algebra · Mathematics 2007-05-23 Adela Vraciu

In this paper we discuss testing for an interaction in the two-way ANOVA with just one observation per cell. The known results are reviewed and a simulation study is performed to evaluate type I and type II risks of the tests. It is shown…

Statistics Theory · Mathematics 2012-07-13 Petr Simecek , Marie Simeckova

This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…

Algebraic Geometry · Mathematics 2015-08-10 János Kollár

Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$…

Operator Algebras · Mathematics 2025-11-04 Kevin Aguyar Brix , Chris Bruce , Kang Li , Eduardo Scarparo

We prove that the $F$-jumping numbers of the test ideal $\tau(X; \Delta, \ba^t)$ are discrete and rational under the assumptions that $X$ is a normal and $F$-finite variety over a field of positive characteristic $p$, $K_X+\Delta$ is…

Algebraic Geometry · Mathematics 2010-05-25 Manuel Blickle , Karl Schwede , Shunsuke Takagi , Wenliang Zhang

We study Torelli-type theorems in the Zariski topology for varieties of dimension at least 2, over arbitrary fields. In place of the Hodge structure, we use the linear equivalence relation on Weil divisors. Using this setup, we prove a…

Algebraic Geometry · Mathematics 2021-01-14 János Kollár , Max Lieblich , Martin Olsson , Will Sawin

For an abelian number field K containing a primitive p-th root of unity (p an odd prime) and satisfying certain technical conditions, we parametrize the Z_p[G(K/Q)]-annihilators of the "minus" part A_K^- of the p-class group by means of…

Number Theory · Mathematics 2010-09-17 Thong Nguyen Quang Do , Vésale Nicolas

The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…

Programming Languages · Computer Science 2013-06-18 Guillaume Allais , Pierre Boutillier , Conor McBride

Continuing ideas of a recent preprint of Schwede arXiv:0906.4313 we study test ideals by viewing them as minimal objects in a certain class of $F$-pure modules over algebras of p^{-e}-linear operators. This shift in the viewpoint leads to a…

Commutative Algebra · Mathematics 2013-08-26 Manuel Blickle

In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual…

Algebraic Geometry · Mathematics 2016-08-29 Manuel Blickle , Axel Stäbler

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

Number Theory · Mathematics 2024-02-02 Jitendra Bajpai , Mattia Cavicchi

Test time adaptation (TTA) aims to adapt deep neural networks when receiving out of distribution test domain samples. In this setting, the model can only access online unlabeled test samples and pre-trained models on the training domains.…

Computer Vision and Pattern Recognition · Computer Science 2023-05-23 Shuai Wang , Daoan Zhang , Zipei Yan , Jianguo Zhang , Rui Li
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