Hodge tate spectial

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August undefined, 2024

Nettet20. jun. 2024 · Further, we give a new proof of the torsion-freeness of the infinitesimal $\mathbb{B}_{\text{dR}}^+$-cohomology independent of Conrad-Gabber spreading theorem, and a conceptual explanation that the degeneration of Hodge-Tate spectral sequences is equivalent to that of Hodge-de Rham spectral sequences. Nettet3 The Hodge-Tate comparison theorem The ﬁrst step to obtain a p-adic Hodge theory was made by J. Tate in 1967 [Ta]. Tate showed, by working with p-divisible groups, that, if A is an abelian variety over K which have good reduction over K, then we have a natural isomorphism H1(A,Q p) ⊗Qp C ∼= (H 1(A,Ω0 A/K) ⊗K C(−1)) ⊕(H0(A,Ω1 A/K ...

HODGE THEORY AND REPRESENTATION THEORY - Institute for …

Nettetis Hodge-Tate if and only if ˚is a semi-simple operator with eigenvalues in Z. The relation ˚= (˚ 1) implies that generalized eigenspace decomposition of H(L) with respect to the endomorphism ˚gives (H(L); ) a structure of a system of Hodge bundles in the sense of [Sim92, Section 4]. By Proposition 1.2, the condition End X K L = Q NettetAccording to Faltings' theorem, the cohomology of any smooth proper variety over a p-adic field is Hodge-Tate (see definition 2.3.4 and theorem 2.2.3 in the Brinon-Conrad lecture notes, math.stanford.edu/~conrad/papers/notes.pdf) so this does not quite match the notions 1-4) (which are closer to "the motive of X is a mixed Tate motive", I guess) st patrick\u0027s day scrambled words with answers

MUMFORD-TATE GROUPS - Institute for Advanced Study

Nettet1 Thus the notion of a Hodge cycle on an abelian variety is intrinsic to the variety: it is a purely algebraic notion. In the case that kDC the theorem shows that the image of a Hodge cycle under an automorphism of C is again a Hodge cycle; equivalently, the notion of a Hodge cycle on an abelian variety over C does not depend on the map X!SpecC. NettetUntil recently, p-adic Hodge theory has featured a wide variety of p-adic periods, but not so many period morphisms.1 The situation changed dramatically with Scholze’s discovery … http://davidrenshawhansen.com/periodmapmod.pdf st patrick\u0027s day scavenger hunt riddles

ag.algebraic geometry - The Mumford-Tate conjecture

Shimura varieties and moduli - James Milne

Nettet17. nov. 2015 · This note explains some of the author’s work on understanding the torsion appearing in the cohomology of locally symmetric spaces such as arithmetic hyperbolic 3-manifolds.The key technical tool was a theory of Shimura varieties with infinite level at p: As p-adic analytic spaces, they are perfectoid, and admit a new kind of period map, … NettetIn mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre ( 1967) introduced and named Hodge–Tate structures using the results of Tate ( 1967) on p-divisible groups . Definition [ edit] Suppose that G is the absolute Galois group of a p -adic field K. rote warn app pcr test kölnNettet4. jan. 2024 · My question is about p-adic Hodge-Tate theory and p-adic Galois representation. What is the definition of $\text{weight or Hodge-Tate weight}$ in the … st patrick\\u0027s day screen print transfers

"Nettet6. mar. 2024 · Hodge–Tate representations are related to certain decompositions of p -adic cohomology theories analogous to the Hodge decomposition, hence the name p -adic Hodge theory. Further developments were inspired by properties of p -adic Galois representations arising from the étale cohomology of varieties. " - Hodge tate spectial

Hodge tate spectial

The relative Hodge-Tate spectral sequence - an overview

http://math.columbia.edu/~chaoli/doc/BhattEilenberg.html Nettet’e is usually called the Mumford-Tate group and M ’the special Mumford-Tate group or Hodge group. Because of the centrality in these lectures of polarized Hodge …

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NettetHONDA-TATE THEORY 3 Theorem 3. If the special bre of S is locally integral then the -ordinary locus is dense in the special bre. We now discuss the problem of classifying A xup to isogeny. For the moduli space of polarized abelian varieties, this is closely related to Honda-Tate theory, which asserts that the isogeny class of an abelian variety ... Nettet’e is usually called the Mumford-Tate group and M ’the special Mumford-Tate group or Hodge group. Because of the centrality in these lectures of polarized Hodge structures, we shall refer to both as Mumford-Tate groups and let the subscripts ’and ’especify to which we are referring. For pure Hodge structures we shall see that M ’e and M

NettetMthat give rise to cuspidal automorphic representations constitute a special. HODGE THEORY AND REPRESENTATION THEORY 3 class of reductive Q-algebraic groups … Nettet8. mar. 2024 · The relative Hodge-Tate spectral sequence -- an overview. Ahmed Abbes, Michel Gros. We give in this note an overview of a recent work leading to a …

NettetThe Relative Hodge–Tate Spectral Sequence: An Overview Ahmed Abbes and Michel Gros 1 Introduction 1.1. Let K be a complete discrete valuation ﬁeld of characteristic 0, … http://www.martinorr.name/blog/2010/09/24/hodge-structures-and-abelian-varieties/

Nettet29. mar. 2024 · The two statements are equivalent by a theorem of Tate ([] theo. 2).Indeed, the cohomology group H 0 (G K, C(1)) vanishes, which implies that the …

Nettet8. mar. 2024 · This book presents two important results in p-adic Hodge theory following the approach initiated by Faltings, namely (i) his main p-adic comparison theorem, and … st patrick\\u0027s day scrapbook paperNettet16. Let X be a (let us say smooth to obscure any confusions I have between H ( X) and H c ( X)) algebraic variety defined over some subfield of C. I have occasionally overheard … rote warn app quarantäneNettetpassage to the special ﬁber on ﬁnite ﬂat group schemes is faithful. Prop. 1.1 says that for p-divisible groups there is no ramiﬁcation restrictions; only the Noetherian hypothesis (which one cannotremove). There is another operation one might consider, namely, passing to the generic ﬁber. The main st patrick\\u0027s day scrambled words with answersNettet20. nov. 2024 · Let $K/{\mathbb {Q}}_p$ be a finite unramified extension with residue field k.In this paper we show that if the Hodge–Tate weights of a crystalline representation $\rho $ of $G_K$ are sufficiently small then these weights are encoded in an explicit way by the reduction of $\rho $ modulo p.Using Fontaine–Laffaille theory this is known for … rote warnlampeNettetLECTURES ON THE HODGE-DE RHAM THEORY OF THE FUNDAMENTAL GROUP OF P1 f0;1;1g RICHARD HAIN Contents 1. Iterated Integrals and Chen’s ˇ1 de Rham Theorem 2 2. Iterated Integrals and Multiple Zeta Numbers 17 3. Mixed Hodge-Tate Structures and Their Periods 24 4. Limit Mixed Hodge Structures and the Drinfeld … rote wand lechtalNettet20. jun. 2024 · Abstract. We prove that the Hodge-Tate spectral sequence of a proper smooth rigid analytic variety can be reconstructed from its infinitesimal $\mathbb {B}_ … rote warn app was ist zu tunNettetrelative Hodge-Tate ﬁltration for proper smooth morphisms of adic spaces that he has developed with Caraiani ([7] 2.2.4). Hyodo has proved the particular case of 2.3 where … rote wasserflöhe