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Showing 1 to 5 of 5 for “"intersection multiplicity"”.
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Asymptotic Behavior of Homology and Intersection Multiplicity
… are primarily concerned with problems related to intersection multiplicity originally introduced by Serre. The characteristic p techniques, especially, the use of the Frobenius functor due to Kunz, Peskine and Szpiro are the major tools in our study. We will present four results. The first one, …
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The Grade Conjecture and asymptotic intersection multiplicity
… Conjecture and its connection with asymptotic intersection multiplicity $\chi_\infty$. Given an $A$-module $M$ of finite projective dimension and a system of parameters $x_1, \ldots, x_r$ for $M$, we show, under certain assumptions on $M$, that $\chi_\infty(M, A/\underline{x}) > 0$. We also …
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Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane
… We provide several different definitions of intersection multiplicity and show that they all agree. Finally, we will use a tropical resultant to determine the intersection multiplicity of points of intersection at infinite distance. Using these new definitions of intersection multiplicity we …
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Determinant, Wall Monodromy and Spherical Functor
… of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.</p>
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p-adic L-functions and the Geometry of Hida Families
… phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating …