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The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
his is a relative result which asserts that the K-theory spectra of any two algebraically closed fields of a given characteristic are equivalent to each other after completion at a prime not e...
Abstract: We present some variants of the Kaplansky condition for a K-Hermite ring $R$ to be an elementary divisor ring; for example, a commutative K-Hermite ring $R$ is an EDR iff for any elements $x...
As a stable analogue of degenerations, we introduce the notion of stable degener-ations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient co...
We present the program boundary, whose source les are available at http://people.sissa.it/~maggiolo/boundary/. Given two natural num-bers g and n satisfying 2g + n 􀀀 2 > 0, the program gener...
We follow the mathematical framework proposed by Bouchut [3] in order to derive equilibrium functions for D1Q3 lattice Boltzmann simulations of the Burgers equation. When a particular convexity proper...
We compute the stable cohomology of the universal Picard stack Pic g ! M g, and also its Picard group. The degree zero Picard stack Pic0 g has homotopy type the classifying space of Kawazumi’s extende...
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on...
We establish a Feynman-Kac-type formula to define fractional Schr\"odinger operators for fractional Kato-decomposable potentials as self-adjoint operators. In this functional integral representation ...
We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local...
We compute, in terms of tautological classes, the fundamental class of the locus of stable hyperelliptic curves, i.e. the closure in the moduli space of stable curves of the locus of smooth hyperellip...
Let $\rho$ be an SRB (or "physical"), measure for the discrete time evolution given by a map $f$, and let $\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter...
In this paper, we develop a one-parameter family of P-stable sixth-order and eighth-order two-step methods with minimal phase-lag errors for numerical integration of second order periodic initial va...
In this paper, some groups ${\rm Ext}_A^{s,t}(Z_p,Z_p)$ with specialized $s$ and $t$ are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the exist...

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