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Sixty-five million years ago, clouds of ash choked the skies over Earth. Dinosaurs, along with about half of all the species on Earth, staggered and died. But in the seas, a colorful population of ma...
The de Rham-Witt and Zp-cohomologies of an algebraic variety     algebraic variety  Zp-cohomologies       font style='font-size:12px;'> 2015/12/10
According to the standard philosophy (cf. Deligne 1994, 3.1), a cohomology theory X 7→ Hi (X, r) on the algebraic varieties over a fixed field k should arise from a functor RΓ taking va...
We compute the Buhler-Reichstein essential dimension of a complex abelian variety using Kummer theory.
THE SPLITTING OF REDUCTIONS OF AN ABELIAN VARIETY     SPLITTING OF REDUCTIONS  ABELIAN VARIETY       font style='font-size:12px;'> 2015/8/26
Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction Av of A modulo v splits up to isogeny. Assumingthe Mumford–Tate conjec...
A Fatou–Bieberbach domain avoiding a neighborhood of a variety of codimension 2.
This study showed that the peach variety Flaminia is self-incompatible in Northern Greece, and it produces fruits only after cross fertilization. Among the peach varieties Doukessa, Fayette, Late Naou...
In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingulariz...
Abstract: We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \cap X^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection from a certain Bott-Samelson variety Z...
Abstract: In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dim...
Abstract: In the case of an almost simple algebraic group $G$ of type $G_2$ over a field of characteristic $p>0$ we study the cohomology modules of line bundles on the flag variety for $G$. Our main r...
Closures of K-orbits in the flag variety for GL(2n)     Closures of K-orbits  flag variety  Representation Theory       font style='font-size:12px;'> 2011/8/23
Abstract: We characterize the O_{2n} orbits in the flag variety for GL_{2n} with rationally smooth closure via a graph-theoretic criterion. We also give a necessary pattern avoidance criterion for rat...
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Sever...
We propose a construction of a tensor exact category Fm X of Artin–Tate motivic sheaves with finite coefficients Z/m over a smooth variety X (over a field K of characteristic prime to m) in terms of &...
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
The toric variety corresponding to the Coxeter fan of type A can also be described as a De Concini-Procesi wonderful model. Using a general result of Rains which relates cohomology of real De Concini-...

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