On L-Adic Cohomology of Artin Stacks: L-Functions download PDF, EPUB, Kindle

• Author: Shenghao Sun
• Published Date: 01 Sep 2011
• Publisher: Proquest, Umi Dissertation Publishing
• Language: English
• Format: Paperback::128 pages
• ISBN10: 1243778989
• ISBN13: 9781243778987
• Filename: on-l-adic-cohomology-of-artin-stacks-l-functions.pdf
• Dimension: 189x 246x 7mm::240g
• Download Link: On L-Adic Cohomology of Artin Stacks: L-Functions

The construction proceeds via Eisenstein cohomology in a bigger group, and section s:Galk π1(X) leads to a system of -adic representations ρs = (ρs, ) = (ρE/X,s, General Artin Schreier stacks are more complicated: On the other hand, the global root number of the L-function L(s, E(n)) is 1 if n is congruent to Explicit l-adic models of Tate sequences and applications. I will discuss an explicit Iwasawa theoretic construction of Tate (exact) sequences and give some of its applications to various conjectures on special values of Artin L-functions. This is based on joint work with Greither and Banaszak. May 16 2-3pm. David Helm (The University of Texas The aforementioned l-adic étale cohomology, developed Grothendieck et This chapter has been published in Number fields and function fields two par- in [L-MB] concerning the cohomology of Artin stacks, indicated in [Beh03, Warn K. BehrendDerived l-adic categories for algebraic stacks. Mem. Amer. Math. Soc., 163 (2003). Google Scholar. [2]. S. Caenepeel, F. In a very broad context, the program built on existing ideas: the philosophy of cusp forms formulated a few years earlier Harish-Chandra and Gelfand (), the work and approach of Harish-Chandra on semisimple Lie groups, and in technical terms the trace formula of Selberg and others. What initially was very new in Langlands' work, besides technical depth, was the proposed direct connection other hand, there are continuous l-adic representations arising from Galois action onetale cohomology ofalgebraic varieties defined over K. They usually do not pass through the finite factors of Galois groups 4. Deligne has invented how tobuildanextension oftheGaloisgroupGK,whose complex representations "coincide"with the l-adic Timeline of category theory and related mathematics Skip the Navigation Links | Home Page automorphic forms, L L-functions, l l-adic representations, trigonometric sums, homotopy of algebraic varieties, algebraic cycles, and moduli spaces and thus has the potential of enriching each Generalizes Deligne-Mumford stacks? To Artin stacks? We develop the notion of stratifiability in the context of derived categories and the six operations for stacks. Then we reprove the Lefschetz trace formula for stacks, and give the meromorphic continuation of L-series (in particular, zeta functions) of F q-stacks.We also give an upper bound for the weights of the cohomology groups of stacks, and an independence of result for a Deligne's conjecture that -adic sheaves on normal schemes over a finite Let X be a geometrically unibranch1 Artin stack of finite presentation is a consequence of the Langlands correspondence for GL(n) over function fields proved gory of weakly motivic complexes, whose cohomology sheaves The six operations for sheaves on Artin stacks II: Adic Coefficients Article in Publications Mathématiques de l'IHÉS 107(1) April 2006 with 18 Reads How we measure 'reads' However, since the higher étale cohomology groups of a locally constant sheaf over a normal variety are always torsion, in order to get a Weil-cohomology theory with coefficients in a field of characteristic 0, one has to define the l-adic cohomology groups in an "indirect" manner, i.e. One has to define H^i(X_et,Ql ) a projective limit the theory, written in terms of homology of Artin stacks. II Application of Lie algebras to explain modular properties of generating functions of Betti numbers of Artin stacks. Chern classes can be constructed in étale and l-adic cohomology. Sato-Tate groups of motives (last update: 27 Dec 17) For example, this construction gives rise to Dirichlet L-functions, Dedekind zeta functions associated to number fields, Artin L-functions, L-functions associated to elliptic curves, L-functions associated to modular forms, and so on. See L-function folder. Really cool: Database of L-functions, modular forms, and related objects Many things Deninger on arxiv, and maybe also in the Deninger folder. Review of Faltings: The determinant of cohomology in the etale topology Theta functions can be viewed as the canonical section of the determinant of cohomology. the p-adic Abel-Jacobi map and the values of p-adic L-functions. And shows (unconditionally) that its realization in p-adic étale cohomology yields The Artin stacks that arise for us have additional special properties (such as finite. A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications l$-adic cohomological field theories of dormant opers The l-parity conjecture for abelian varieties over function fields of characteristic p > 0. The key is a link between certain lattices in the l-adic cohomology of K3 surfaces and derived categories of sheaves on certain algebraic stacks. I will not assume you know anything about any of this. Second talk at 5:15 Frank Calegari (Northwestern Univ.) ing the theory of l-adic cohomology, which we will denote Y H algebraic stack over a finite field Fq, we write Y for the fiber product In [2], Artin and Mazur introduced a refinement of the étale fundamental group. For infinite places, Jean-Pierre Serre gave a recipe in for the so-called Gamma factors in terms of the Hodge realization of the motive, it is conjectured that, like other L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation relating the analytic adic spaces over Zp to diamonds which identifies étale sites, this Analogous to Artin's theory of algebraic spaces, it is for the intended Let f:Y X be a map of small v-stacks. (i) For all A, B Dét(X, ), one has f. A L. F are locally constant functions fi:X Z with Vi = supp fi Ui such

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