scholarly journals A Lefschetz trace formula for equivariant cohomology

1995 ◽  
Vol 28 (6) ◽  
pp. 669-688 ◽  
Author(s):  
Minhyong Kim
Keyword(s):  
Trace Formula ◽  
Equivariant Cohomology ◽  
Lefschetz Trace Formula

scholarly journals On the Lefschetz trace formula for Lubin–Tate spaces

2016 ◽  
Vol 16 (1) ◽  
Author(s):  
Xu Shen
Keyword(s):  
Trace Formula ◽  
Unitary Group ◽  
Locally Finite ◽  
Lefschetz Trace Formula ◽  
Cell Decompositions ◽  
Finite Cell

AbstractWe give a new proof of the Lefschetz trace formula for Lubin-Tate spaces. Our proof is based on the locally finite cell decompositions of these spaces and on Mieda’s version of the Lefschetz trace formula for certain open adic spaces. This proof is rather different from the proofs of Strauch and Mieda, and it might be generalized to other Rapoport-Zink spaces as soon as there exist suitable cell decompositions. For example, in another paper we have proved a Lefschetz trace formula for some unitary group Rapoport-Zink spaces by using similar ideas as here.

LEFSCHETZ TRACE FORMULA AND BRST

1989 ◽  
Vol 04 (20) ◽  
pp. 1891-1897 ◽  
Author(s):  
A.S. SCHWARZ
Keyword(s):  
Trace Formula ◽  
Constrained System ◽  
Lefschetz Trace Formula

The reduction of quantum constrained system to the unconstrained system with ghosts is analyzed.

The Trace Formula for BunG(X)

2019 ◽  
pp. 239-308
Author(s):  
Dennis Gaitsgory ◽  
Jacob Lurie
Keyword(s):  
Trace Formula ◽  
Algebraic Curve ◽  
Group Scheme ◽  
Affine Group ◽  
Generic Fiber ◽  
Prove Theorem ◽  
Lefschetz Trace Formula ◽  
Moduli Stack ◽  
Smooth Affine

This chapter aims to prove Theorem 1.4.4.1, which is formulated as follows: Theorem 5.0.0.3, let X be an algebraic curve over F q and let G be a smooth affine group scheme over X. Suppose that the fibers of G are connected and that the generic fiber of G is semisimple. Then the moduli stack BunG(X) satisfies the Grothendieck–Lefschetz trace formula. However, Theorem 5.0.0.3 cannot be deduced directly from the Grothendieck–Lefschetz trace formula for global quotient stacks because the moduli stack BunG(X) is usually not quasi-compact. The strategy instead will be to decompose BunG (X) into locally closed substacks BunG(X)[P,ν‎] which are more directly amenable to analysis.

scholarly journals Cubic Twin Prime Polynomials are Counted by a Modular Form

2019 ◽  
Vol 71 (6) ◽  
pp. 1323-1350
Author(s):  
Lior Bary-Soroker ◽  
Jakob Stix
Keyword(s):  
Modular Form ◽  
Elliptic Curve ◽  
Trace Formula ◽  
Twin Primes ◽  
Lefschetz Trace Formula

AbstractWe present the geometry behind counting twin prime polynomials in $\mathbb{F}_{q}[T]$ in general. We compute cohomology and explicitly count points by means of a twisted Lefschetz trace formula applied to these parametrizing varieties for cubic twin prime polynomials. The elliptic curve $X^{3}=Y(Y-1)$ occurs in the geometry, and thus counting cubic twin prime polynomials involves the associated modular form. In theory, this approach can be extended to higher degree twin primes, but the computations become harder.The formula we get in degree 3 is compatible with the Hardy–Littlewood heuristic on average, agrees with the prediction for $q\equiv 2$ (mod 3), but shows anomalies for $q\equiv 1$ (mod 3).

Sign in / Sign up

Export Citation Format

Share Document