partial regularity and amplitude the author continues the study of frobenius amplitude introduced in an earlier paper and compares this to various other positivity notions these are applied to deduce vanishing theorems a refinement of castelnuovo mumford regularity is also given

controller discretization a gap metric framework for analysis and synthesis although techniques for directly synthesising sampled data sd compensators are available in the literature feedback controller design is perhaps best understood in a purely continuous time setting as such a feedback controller is often designed in the continuous time domain and then discretized for digital implementation it is important for the discretization step involved to yield an sd approximation which captures the essential features of the original controller from the perspective of closed loop behavior in this note a gap metric framework is developed for studying the controller discretization problem for linear time invariant lti plants and controllers importantly knowledge of a gap metric distance between an lti controller and an sd approximation permits explicit characterization of the possible difference in closed loop performance with any lti plant for which the lti controller is known to work well accounting for intersample behavior the central result of the new framework gives rise to an algorithm for computing a gap metric measure of the distance between an lti controller and a given discretization and a technique for synthesising a sd approximation which is optimal with respect to this metric

degeneration of l adic weight spectral sequences the degeneracy of the l adic weight spectral sequence over any trait with no assumptions on its residue field is proved by the method of log geometry in the sense of fontaine illusie

frobenius amplitude and strong vanishing theorems for vector bundles the primary goal of this paper is to systematically exploit the method of deligne illusie to obtain kodaira type vanishing theorems for vector bundles and more generally coherent sheaves on algebraic varieties the key idea is to introduce a number which provides a cohomological measure of the positivity of a coherent sheaf called the frobenius or f amplitude the f amplitude enters into the statement of the basic vanishing theorem and this leads to the problem of calculating or at least estimating this number most of the work in this paper is devoted to doing this various situations

vanishing theorems for torsion automorphic sheaves on general pel type shimura varieties abstract we consider the interior cohomology and the hodge graded pieces in the case of the de rham realization of general not necessarily compact pel type shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group for primes p bigger than an effective bound we prove that the f p and z p cohomology groups are concentrated in the middle degree that the z p cohomology groups are free of p torsion and that every f p cohomology class lifts to a z p cohomology class

cohomology of p adic stein spaces we compute p adic etale and pro etale cohomologies of drinfeld half spaces in the pro etale case the main input is a comparison theorem for p adic stein spaces the cohomology groups involved here are much bigger than in the case of etale cohomology of algebraic varieties or proper analytic spaces considered in all previous works in the etale case the classical p adic comparison theorems allow us to pass to a computation of integral differential forms cohomologies which can be done because the standard formal models of drinfeld half spaces are pro ordinary and their differential forms are acyclic

localization in a spanwise extended model of plane couette flow we consider a nine partial differential equation 1 space and 1 time model of plane couette flow in which the degrees of freedom are severely restricted in the streamwise and cross stream directions to study spanwise localization in detail of the many steady eckhaus spanwise modulational instabilities identified of global steady states none lead to a localized state spatially localized time periodic solutions were found instead which arise in saddle node bifurcations in the reynolds number these solutions appear global domain filling in narrow small spanwise domains yet can be smoothly continued out to fully spanwise localized states in very wide domains this smooth localization behavior which has also been seen in fully resolved duct flow s okino ph d thesis kyoto university kyoto 2011 indicates that an apparently global flow structure does not have to suffer a modulational instability to localize in wide domains

integral crystalline cohomology over very ramified valuation rings in this paper we intend to show how fontaine s comparison theory fol fo2 between crystalline and p adic etale cohomology can be extented to very ramified base rings so far it had been developed either for qp coefficients or zp coefficients if the base is unramified over the witt vectors see fa2 for example it states that for any p adic discrete valuation ring v there exists a ring b v with the following property if x denotes a smooth and proper v scheme the p adic etale cohomology of the generic fiber x xv k is related to the crystalline cohomology of x v0 vo defined below by an isomorphism

semiregularity and obstructions of complete intersections abstract we prove that on a smooth projective variety over an algebraically closed field of characteristic 0 the semiregularity map annihilates every obstruction to embedded deformations of a local complete intersection subvariety with extendable normal bundle the proof is based on the theory of l algebras and tamarkin tsygan calculus on the de rham complex of dg schemes

on the p adic local invariant cycle theorem for a proper flat generically smooth scheme x over a complete discrete valuation ring with finite residue field of characteristic p we construct a specialization morphism from the rigid cohomology of the geometric special fibre to d cris of the p adic etale cohomology of the geometric generic fibre and we make a conjecture p adic local invariant cycle theorem that describes the behavior of this map for regular x analogous to the situation in ell adic etale cohomology for ell ne p our main result is that if x has semistable reduction this specialization map induces an isomorphism on the slope 0 1 part

on a large gain theorem the aim of this paper is to give a general quantitative requirement which the loop gain must satisfy in order to stabilize a given unstable possibly nonlinear and time varying plant namely that the gain must exceed one

logarithmic hodge witt sheaves on normal crossing varieties in this paper we define two kinds homological and cohomological of etale logarithmic hodge witt sheaves on normal crossing varieties over a perfect field of positive characteristic and discuss some fundamental properties in particular puity and duality

mimo nyquist interpretation of the large gain theorem the large gain theorem is an input output stability result with intriguing applications in the field of control systems this paper aims to increase understanding and appreciation of the large gain

syntomic complexes and p adic nearby cycles we compute syntomic cohomology of semistable affinoids in terms of cohomology of varphi gamma modules which thanks to work of fontaine herr andreatta iovita and kedlaya liu is known to compute galois cohomology of these affinoids for a semistable scheme over a mixed characteristic local ring this implies a comparison isomorphism up to some universal constants between truncated sheaves of p adic nearby cycles and syntomic cohomology sheaves this generalizes the comparison results of kato kurihara and tsuji for small tate twists where no constants are necessary as well as the comparison result of tsuji that holds over the algebraic closure of the field as an application we combine this local comparison isomorphism with the theory of finite dimensional banach spaces and finiteness of etale cohomology of rigid analytic spaces proved by scholze to prove a semistable conjecture for formal schemes with semistable reduction

vanishing via lifting to second witt vectors and a proof of an isotriviality result abstract a proof based on reduction to finite fields of esnault and viehweg s stronger version of the sommese vanishing theorem for k ample line bundles is given this result is used to give different proofs of isotriviality results of parshin and migliorini

a relation between the parabolic chern characters of the de rham bundles in this paper we consider the weight i de rham gauss manin bundles on a smooth variety arising from a smooth projective morphism f x u longrightarrow u for i geq 0 we associate to each weight i de rham bundle a certain parabolic bundle on s and consider their parabolic chern characters in the rational chow groups for a good compactification s of u we show the triviality of the alternating sum of these parabolic bundles in the positive degree rational chow groups this removes the hypothesis of semistable reduction in the original result of this kind due to esnault and viehweg

laminar turbulent boundary in plane couette flow we apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane couette flow at re 400 perturbations that are not strong enough to become fully turbulent or weak enough to relaminarize tend toward a hyperbolic coherent structure in state space termed the edge state which seems to be unique up to obvious continuous shift symmetries the results reported here show that in cases where a fixed point has only one unstable direction such as for the lower branch solution in plane couette flow the iterated edge tracking algorithm converges to this state they also show that the choice of initial state is not critical and that essentially arbitrary initial conditions can be used to find the edge state

toric singularities revisited abstract in k kato toric singularities amer j math 116 5 1994 1073 1099 kato defined his notion of a log regular scheme and studied the local behavior of such schemes a toric variety equipped with its canonical logarithmic structure is log regular and these schemes allow one to generalize toric geometry to a theory that does not require a base field this paper will extend this theory by removing normality requirements

rigid cohomology and invariant cycles for a semistable log scheme introduction let k be a perfect field of characteristic p 0 we indicate by w the ring of witt vectors of k and by k0 its quotient field the study of cohomological theories like rigid or crystalline cohomology encounters some problems when applied to singular k varieties in this paper we deal with the rigid cohomology of a particular type of singular k varieties recently a new theory log crystalline cohomology has provided a way to associate to a proper semistable k l log scheme y m the cohomology groups

quasi frobenius splitting and lifting of calabi yau varieties in characteristic p generalizing the notion of frobenius splitting we prove that every finite height calabi yau variety defined over an algebraically closed field of positive characteristic can be lifted to the ring of witt vectors of length two

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

on p adic intermediate jacobians for an algebraic variety of dimension with totally degenerate reduction over a adic field definition recalled below and an integer with we define a rigid analytic torus together with an abel jacobi mapping to it from the chow group of codimension algebraic cycles that are homologically equivalent to zero modulo rational equivalence these tori are analogous to those defined by griffiths using hodge theory over we compare and contrast the complex and adic theories finally we examine a special case of a adic analogue of the generalized hodge conjecture

a dynamic solver consistent minimum action method this paper discusses the necessity and strategy to unify the development of a dynamic solver and a minimum action method mam for a spatially extended system when employing the large deviation principle ldp to study the effects of small random perturbations a dynamic solver is used to approximate the unperturbed system and a minimum action method is used to approximate the ldp which corresponds to solving an euler lagrange equation related to but more complicated than the unperturbed system we will clarify possible inconsistencies induced by independent numerical approximations of the unperturbed system and the ldp based on which we propose to define both the dynamic solver and the mam on the same approximation space for spatial discretization the semi discrete ldp can then be regarded as the exact ldp of the semi discrete unperturbed system which is a finite dimensional ode system we achieve this methodology for the two dimensional navier stokes equations using a divergence free approximation space the method developed can be used to study the nonlinear instability of wall bounded parallel shear flows and be generalized straightforwardly to three dimensional cases numerical experiments are presented

landau ginzburg hodge numbers for mirrors of del pezzo surfaces abstract we consider the conjectures from 10 about landau ginzburg hodge numbers associated to tamely compactifiable landau ginzburg models we test these conjectures in case of dimension two verifying some and giving a counterexample to the other

classicite en theorie de hida in this article we prove an effective classicity theorem in hida s theory we focus more precisely on the case of the symplectic group and siegel modular forms we also prove that certain mod p siegel modular forms lift to characteristic zero and study carefully the divisibility by p of certain hecke operators